Fungi
N. J. A. Sloane
njas at research.att.com
Sat Jun 23 23:45:21 CEST 2007
Neil,
<< it seems to me a(11) = -1 since 2^11 = 2048 >>
Agreed. I don't get it ... ?:-/
'Sorry if this has already been addressed ... but is there any significance
to the differences in the PARI code given for A124691 and A124692, i.e.,
digitpos2ton(n) = \ 2^n expansion first occurrence of n { local(x, y, r,
dot); for(x=0, n, r = 2^x; ...
vs.
digitposmton(n, m) = \ m^n expansion first occurrence of n { local(x, y,
r, dot); for(x=0, n, r = m^x; ...
(Does the PARI code for either one yield a sequence anything like the
enigmatic "-1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,4, ..."?)
(For what it's worth, 51^11 = 6071163615208263051, which has the substring
"11" starting at the 4th digit, and 51 is the smallest positive integer for
which this is the case.)
-- Jon
----- Original Message -----
From: "N. J. A. Sloane" <njas at research.att.com>
To: <seqfan at ext.jussieu.fr>
Cc: <hillcino368 at hotmail.com>; <njas at research.att.com>
Sent: Saturday, June 23, 2007 3:03 PM
Subject: help needed with a duplicate
> Dear Seqfans, Andrew P. pointed out that A124691 and A124692
> were the same. So I tried to edit A124692.
> The old entry was :
>
> %I A124692
> %S A124692
> 1,1,1,1,1,1,1,1,1,1,1,4,4,4,5,5,5,6,6,6,7,7,7,7,8,8,8,9,9,9,10,10,10,10,11,3,
> %T A124692
> 10,2,12,12,13,13,13,13,10,14,14,15,15,5,16,3,16,16,17,17,17,18,18,18,11,19,19,19,20,
> %U A124692
> 20,20,13,21,21,22,22,2,5,23,23,23,24,24,24,25,25,20,25,26,4,26,27,27,3,28,28,28,24,29
> %V
> A124692 -1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,4,4,4,5,5,5,6,6,6,7,7,7,7,8,8,8,9,9,9,10,10,10,10,11,3,
> %W A124692
> 10,2,12,12,13,13,13,13,10,14,14,15,15,5,16,3,16,16,17,17,17,18,18,18,11,19,19,19,20,
> %X A124692
> 20,20,13,21,21,22,22,2,5,23,23,23,24,24,24,25,25,20,25,26,4,26,27,27,3,28,28,28,24,29
> %N A124692 Position of the first n in the expansion of 2^n, or -1 if the
> digits of n never appear.
> %o A124692 (PARI) digitposmton(n,m) = \ m^n expansion first occurrence of
> n { local(x,y,r,dot); for(x=0,n, r = m^x; if(r==floor(r),
> y=find(Str(floor(r)),x), y=find(Str(r),x); dot=find(Str(r),"."); if(dot <
> y, y--); ); if(y, print1(y","),print1(-1",") ) )
> find(str,match) = \Return the position of the first occurrence of string
> \match in string str { local(lnm,lns,x,c,i); str=Str(str); \This allows
> leaving quotes off input match=Str(match); c=0; i=0; lns=length(str);
> lnm=length(match); if(lnm>1,i=1); x=1;
> if(x>lns,return(0),return(x)) } mid(str,s,n) = \ Get a substring of length
> n from string str starting at position s in str. { local(v,ln,x,tmp); v
> =""; tmp = Vec(str); ln=length(tmp); for(x=s,s+n-1, v=concat(v,tmp[x]); );
> return(v) }
> %K A124692 base,easy,sign
> %O A124692 0,12
> %A A124692 Cino Hilliard (hillcino368(AT)hotmail.com), Dec 25 2006
>
> I tried to edit the description to the following:
>
> %N A124692 Starting position of the first n in the decimal expansion of
> 2^n, reading the decimal string "2^n" from left to right; or -1 if the
> digits of n never appear.
>
> and added some examples:
>
> %e A124692 2^6 = 64, where "6" appears in position 1, so a(6) = 1.
> %e A124692 2^10 = 1024, so a(10) = 1.
> %e A124692 But why is a(11) = 4?
>
> it seems to me a(11) = -1 since 2^11 = 2048
>
> What am I missing?
>
> Neil
>
>
> it seems to me a(11) = -1 since 2^11 = 2048
For terms greater than a(10), whenever the digits of n never appear,
Cino's list sports the number of digits in 2^n, instead of -1. It's
possible that this is just an erroneous output from his coding, but I
cannot confirm this since I do not speak PARI. There is no reason why
we cannot use 0 instead of -1, thus removing the sequence from the
In Mathematica, I used:
t = {}; Do[s = StringPosition[ToString[2^n], ToString[n]]; If[s ==
{}, t = Append[t, 0], t = Append[t, s[[1]][[1]]]], {n, 0, 999}]; t
... to get:
{0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 10, 2, 0, 0, 0, 0, 0, 0, 10,
0, 0, 0, 0, 5, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0,
13, 0, 0, 0, 0, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 4, 0, 0, 0,
3, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 0,
0, 0, 0, 0, 0, 0, 0, 5, 0, 17, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
35, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0,
0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 17,
30, 0, 0, 0, 0, 0, 0, 0, 117, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0,
66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 14, 0, 0, 57, 62, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0,
25, 0, 81, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 143, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 2, 92, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 122, 0, 0, 113, 0, 129, 0, 0,
0, 0, 0, 93, 0, 0, 0, 20, 0, 0, 0, 0, 0, 159, 0, 0, 0, 0, 0, 0, 0,
138, 0, 0, 0, 0, 187, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0,
0, 0, 0, 0, 57, 35, 0, 105, 0, 0, 0, 0, 158, 9, 0, 0, 0, 0, 50, 0, 0,
0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 185, 0, 0, 182, 0, 42, 0, 17, 0, 196, 0, 0, 0, 0, 0, 0, 0,
0, 0, 19, 0, 0, 0, 0, 0, 93, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 107, 0,
0, 0, 0, 0, 220, 0, 0, 0, 0, 0, 40, 0, 0, 5, 0, 0, 0, 0, 25, 0, 0,
142, 187, 0, 0, 0, 0, 217, 0, 0, 0, 127, 0, 0, 0, 0, 78, 27, 0, 0, 0,
47, 0, 0, 0, 72, 5, 141, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 236, 0, 0, 0, 0, 93,
0, 0, 0, 0, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 185, 0,
212, 0, 0, 0, 203, 0, 0, 0, 0, 56, 0, 0, 0, 32, 0, 78, 218, 0, 0, 0,
0, 0, 0, 124, 55, 0, 0, 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
246, 0, 79, 0, 0, 0, 0, 66, 0, 0, 68, 0, 0, 0, 0, 154, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 179, 0, 246, 0, 0, 0, 0, 0, 131, 0, 0, 0, 115, 157,
137, 150, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 253, 0, 0, 242, 0, 0, 0,
164, 0, 0, 0, 58, 0, 51, 0, 243, 0, 0, 62, 187, 0, 27, 0, 0, 139,
171, 0, 0, 279, 0, 0, 0, 0, 0, 0, 0, 0, 249, 0, 0, 0, 0, 212, 193, 0,
0, 0, 0, 0, 0, 0, 276, 0, 202, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0,
0, 0}
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