[seqfan] Re: Nice nontrivial integer sequence
Fred Lunnon
fred.lunnon at gmail.com
Tue Mar 7 02:47:27 CET 2023
sequ := // extracted stable sequence: 102 terms. via Chai Wah Wu
[ 1, 4, 11, 29, 47, 18, 61, 165, 434, 703, 1675, 972, 2213, 10093, 17973,
25853,
59586, 33733, 7880, 21427, 56401, 204177, 147776, 91375, 217724, 126349,
414021,
287672, 161323, 34974, 48521, 13547, 5667, 9121, 12575, 28604, 16029, 3454,
1241, 269, 1180, 3271, 2091, 911, 2464, 11409, 20354, 90361, 250729,
160368,
551111, 1492965, 941854, 390743, 1011861, 621118, 2714847, 15667964,
44289045,
161488216, 278687387, 117199171, 72910126, 174441333, 450413873, 275972540,
101531207, 28621081, 12953117, 36144504, 23191387, 33429657, 10238270,
7523423,
19855422, 52042843, 32187421, 44519420, 12331999, 4808576, 21328033,
59175523,
156198536, 253221549, 350244562, 97023013, 231893516, 134870503, 37847490,
16519457, 61269252, 167288299, 273307346, 106019047, 362806936, 1345208697,
3672819155, 6000429613, 2327610458, 982401761, 1601996586, 5425584583 ];
On Mon, Mar 6, 2023 at 6:54 PM Chai Wah Wu <cwwuieee at gmail.com> wrote:
> I ran Christian's program (with Brendan's modifications) a little longer
> and got:
>
> stable no. 97 is 3672819155 after 5018027852 terms
> 2 is at 5142
> stable no. 98 is 6000429613 after 9673248768 terms
> stable no. 99 is 2327610458 after 9673248768 terms
> stable no. 100 is 982401761 after 9673248768 terms
> stable no. 101 is 1601996586 after 9673248768 terms
> stable no. 102 is 5425584583 after 9673248768 terms
> 2 is at 5888
> after 10000000000u terms:
> 2 is at 5930
>
>
> On Sun, Mar 5, 2023 at 11:35 PM Brendan McKay via SeqFan <
> seqfan at list.seqfan.eu> wrote:
>
> > Without understanding a thing, I defined T as "unsigned long long",
> > N as "5000000000ULL" and changed "%u" to "%llu%. Then I ran it
> > on a computer with 128GB. It took 12 minutes. Here is all the output.
> > It looks like it isn't much use??
> >
> > Brendan
> >
> >
> -------------------------------------------------------------------------------------------
> >
> > stable no. 2 is 4 after 5 terms
> > 2 is at 5
> > stable no. 3 is 11 after 15 terms
> > 2 is at 10
> > stable no. 4 is 29 after 40 terms
> > 2 is at 17
> > stable no. 5 is 47 after 76 terms
> > stable no. 6 is 18 after 76 terms
> > 2 is at 25
> > stable no. 7 is 61 after 79 terms
> > 2 is at 25
> > stable no. 8 is 165 after 226 terms
> > 2 is at 39
> > stable no. 9 is 434 after 599 terms
> > 2 is at 57
> > stable no. 10 is 703 after 1137 terms
> > 2 is at 74
> > stable no. 11 is 1675 after 2378 terms
> > 2 is at 96
> > stable no. 12 is 972 after 2647 terms
> > 2 is at 102
> > stable no. 13 is 2213 after 3185 terms
> > 2 is at 106
> > stable no. 14 is 10093 after 12306 terms
> > 2 is at 176
> > stable no. 15 is 17973 after 28066 terms
> > 2 is at 234
> > stable no. 16 is 25853 after 43826 terms
> > 2 is at 268
> > stable no. 17 is 59586 after 85439 terms
> > 2 is at 331
> > stable no. 18 is 33733 after 93319 terms
> > stable no. 19 is 7880 after 93319 terms
> > stable no. 20 is 21427 after 93319 terms
> > stable no. 21 is 56401 after 93319 terms
> > 2 is at 341
> > stable no. 22 is 204177 after 260578 terms
> > 2 is at 475
> > stable no. 23 is 147776 after 351953 terms
> > stable no. 24 is 91375 after 351953 terms
> > stable no. 25 is 217724 after 351953 terms
> > stable no. 26 is 126349 after 351953 terms
> > 2 is at 513
> > stable no. 27 is 414021 after 540370 terms
> > 2 is at 574
> > stable no. 28 is 287672 after 701693 terms
> > stable no. 29 is 161323 after 701693 terms
> > stable no. 30 is 34974 after 701693 terms
> > stable no. 31 is 48521 after 701693 terms
> > stable no. 32 is 13547 after 701693 terms
> > stable no. 33 is 5667 after 701693 terms
> > stable no. 34 is 9121 after 701693 terms
> > stable no. 35 is 12575 after 701693 terms
> > stable no. 36 is 28604 after 701693 terms
> > stable no. 37 is 16029 after 701693 terms
> > stable no. 38 is 3454 after 701693 terms
> > stable no. 39 is 1241 after 701693 terms
> > stable no. 40 is 269 after 701693 terms
> > stable no. 41 is 1180 after 701693 terms
> > stable no. 42 is 3271 after 701693 terms
> > stable no. 43 is 2091 after 701693 terms
> > stable no. 44 is 911 after 701693 terms
> > stable no. 45 is 2464 after 701693 terms
> > stable no. 46 is 11409 after 701693 terms
> > stable no. 47 is 20354 after 701693 terms
> > stable no. 48 is 90361 after 701693 terms
> > stable no. 49 is 250729 after 701693 terms
> > stable no. 50 is 160368 after 701693 terms
> > 2 is at 622
> > stable no. 51 is 551111 after 711479 terms
> > 2 is at 624
> > stable no. 52 is 1492965 after 2044076 terms
> > 2 is at 825
> > stable no. 53 is 941854 after 2434819 terms
> > stable no. 54 is 390743 after 2434819 terms
> > stable no. 55 is 1011861 after 2434819 terms
> > stable no. 56 is 621118 after 2434819 terms
> > 2 is at 873
> > stable no. 57 is 2714847 after 3335965 terms
> > 2 is at 955
> > stable no. 58 is 15667964 after 18382811 terms
> > 2 is at 1490
> > stable no. 59 is 44289045 after 59957009 terms
> > 2 is at 1969
> > stable no. 60 is 161488216 after 205777261 terms
> > 2 is at 2599
> > stable no. 61 is 278687387 after 440175603 terms
> > stable no. 62 is 117199171 after 440175603 terms
> > stable no. 63 is 72910126 after 440175603 terms
> > stable no. 64 is 174441333 after 440175603 terms
> > 2 is at 3074
> > stable no. 65 is 450413873 after 624855206 terms
> > 2 is at 3311
> > stable no. 66 is 275972540 after 726386413 terms
> > stable no. 67 is 101531207 after 726386413 terms
> > stable no. 68 is 28621081 after 726386413 terms
> > stable no. 69 is 12953117 after 726386413 terms
> > stable no. 70 is 36144504 after 726386413 terms
> > stable no. 71 is 23191387 after 726386413 terms
> > stable no. 72 is 33429657 after 726386413 terms
> > stable no. 73 is 10238270 after 726386413 terms
> > stable no. 74 is 7523423 after 726386413 terms
> > stable no. 75 is 19855422 after 726386413 terms
> > stable no. 76 is 52042843 after 726386413 terms
> > stable no. 77 is 32187421 after 726386413 terms
> > stable no. 78 is 44519420 after 726386413 terms
> > stable no. 79 is 12331999 after 726386413 terms
> > stable no. 80 is 4808576 after 726386413 terms
> > stable no. 81 is 21328033 after 726386413 terms
> > stable no. 82 is 59175523 after 726386413 terms
> > stable no. 83 is 156198536 after 726386413 terms
> > stable no. 84 is 253221549 after 726386413 terms
> > stable no. 85 is 350244562 after 726386413 terms
> > stable no. 86 is 97023013 after 726386413 terms
> > stable no. 87 is 231893516 after 726386413 terms
> > stable no. 88 is 134870503 after 726386413 terms
> > stable no. 89 is 37847490 after 726386413 terms
> > stable no. 90 is 16519457 after 726386413 terms
> > stable no. 91 is 61269252 after 726386413 terms
> > stable no. 92 is 167288299 after 726386413 terms
> > stable no. 93 is 273307346 after 726386413 terms
> > stable no. 94 is 106019047 after 726386413 terms
> > stable no. 95 is 362806936 after 726386413 terms
> > 2 is at 3416
> > stable no. 96 is 1345208697 after 1708015633 terms
> > 2 is at 4091
> > after 5000000000 terms:
> > 2 is at 5140
> >
> >
> >
> >
> >
> > On 3/6/23 09:27, Arthur O'Dwyer wrote:
> > > I confirm these results, using a C++ program that I wrote without
> looking
> > > at Christian's C program. (Now I've looked, and I think we converged to
> > the
> > > same basic data structures... except that Christian doesn't even need
> to
> > > store the list of `i` values? Ah, yes, now I see; that's clever.
> Updated
> > > mine.)
> > > https://quuxplusone.github.io/blog/2023/03/05/oeis-a360447/
> > > has my C++ program and results up to a(96), at which point I, also, run
> > out
> > > of memory.
> > >
> > > –Arthur
> > >
> > > On Thu, Mar 2, 2023 at 7:15 AM Christian Sievers<seqfan at duvers.de>
> > wrote:
> > >
> > >> Hello,
> > >>
> > >> it seems like the list doesn't allow attachments, so I put (the latest
> > >> version of) my program at the end of this mail.
> > >>
> > >> For the next billion terms I changed the type to unsigned integers.
> > >> To go even further one could use (unsigned) *long* ints, but that's
> too
> > >> much for my 32G memory.
> > >>
> > >> My only new results (still took only 48 seconds) are these:
> > >>
> > >> stable no. 96 is 1345208697 after 1708015633 terms
> > >> 2 is at 4091
> > >> after 2000000000 terms:
> > >> 2 is at 4222
> > >>
> > >> All the best
> > >> Christian
> > >> ------------------------------------------------
> > >>
> > >> #include<stdio.h>
> > >> #include<stdlib.h>
> > >> #include<assert.h>
> > >>
> > >> #define N 2000000000
> > >>
> > >> typedef unsigned int T;
> > >>
> > >> T *next;
> > >> T *sum;
> > >>
> > >> void update_sum(T n, T o){
> > >> T s, d, od, tp;
> > >> s = n+o;
> > >> d = (n>o) ? n-o : o-n;
> > >> tp=2*sum[s];
> > >> if(!tp){
> > >> sum[s]=n;
> > >> return;
> > >> }
> > >> od = (s>tp) ? s-tp : tp-s;
> > >> if (d<od)
> > >> sum[s]=n;
> > >> }
> > >>
> > >> void report(T s, T i){
> > >> static T count=1;
> > >> printf("stable no. %u is %u after %u terms\n", ++count, s, i);
> > >> }
> > >>
> > >> void report2(void){
> > >> T p,c;
> > >> p=c=1;
> > >> while(p!=2){
> > >> p=next[p];
> > >> ++c;
> > >> }
> > >> printf("2 is at %u\n", c);
> > >> }
> > >>
> > >> int main(void){
> > >> T last,stable,need,i,p,q;
> > >> next=calloc(N+1u, sizeof(T));
> > >> assert(next);
> > >> sum=calloc(2u*N, sizeof(T));
> > >> assert(sum);
> > >> last=1;
> > >> stable=1;
> > >> need=5;
> > >> for(i=2; i<=N; ++i){
> > >> p=sum[i];
> > >> if(p){
> > >> q=next[p];
> > >> next[p]=i;
> > >> next[i]=q;
> > >> update_sum(p,i);
> > >> update_sum(i,q);
> > >> if (p==stable)
> > >> need=p+i;
> > >> } else {
> > >> next[last]=i;
> > >> update_sum(last,i);
> > >> last=i;
> > >> }
> > >> if (i==need){
> > >> while(i>=need){
> > >> stable=next[stable];
> > >> need=stable+next[stable];
> > >> report(stable,i);
> > >> }
> > >> report2();
> > >> }
> > >> }
> > >> printf("after %u terms:\n", N);
> > >> report2();
> > >> }
> > >>
> > >> --
> > >> Seqfan Mailing list -http://list.seqfan.eu/
> > >>
> > > --
> > > Seqfan Mailing list -http://list.seqfan.eu/
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
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