[seqfan] FW: Re: More stupid thingies with commas, sums & primes
Christopher Hunt gribble
cgribble263 at btinternet.com
Wed Oct 19 17:04:47 CEST 2011
The ways in which prime sums can be formed from the least significant digit
(LSD) of a(n-1) and the most significant digit (MSD) of a(n) are:
2 0 + 2, 1 + 1
3 0 + 3, 1 + 2, 2 + 1
5 0 + 5, 1 + 4, 2 + 3, 3 + 2, 4 + 1
7 0 + 7, 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1
11 2 + 9, 3 + 8, 4 + 7, 5 + 6, 6 + 5, 7 + 4, 8 + 3, 9 + 2
13 4 + 9, 5 + 8, 6 + 7, 7 + 6, 8 + 5, 9 + 4
17 8 + 9, 9 + 8
These partitions are not uniformly distributed as can be seen from their
frequencies in the first 9999 pairs.
MSD 0 1 2 3 4 5 6 7 8
9
LSD
0 0 0 273 219 0 225 0 284 0 0
1 0 500 1 0 198 0 303 0 0 0
2 0 263 0 209 0 227 0 0 0 302
3 0 0 323 0 207 0 0 0 471 0
4 0 264 0 209 0 0 0 511 0 17
5 0 0 325 0 0 0 507 0 168 0
6 0 280 0 0 0 436 0 284 0 0
7 0 0 0 0 698 0 301 0 0
0
8 0 0 0 474 0 223 0 0 0 300
9 0 0 321 0 204 0 0 0 472 0
Chris
-----Original Message-----
From: Christopher Hunt gribble [mailto:cgribble263 at btinternet.com]
Sent: 19 October 2011 1:34 PM
To: 'Sequence Fanatics Discussion list'
Subject: RE: [seqfan] Re: More stupid thingies with commas, sums & primes
Oh bother! I put the frequency counting bit in the wrong loop.
Here are the correct (9999) prime sum frequencies:
2 773
3 483
5 1219
7 1835
11 3720
13 1197
17 772
Chris
-----Original Message-----
From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
On Behalf Of Eric Angelini
Sent: 19 October 2011 1:23 PM
To: Sequence Fanatics Discussion list
Cc: Jean-Marc Falcoz; Alexandre Wajnberg
Subject: [seqfan] Re: More stupid thingies with commas, sums & primes
Thanks, Chris !
Best,
É.
> The first 99 terms are:
1, 2, 3, 4, 7, 6, 5, 8, 9, 20,
21, 10, 22, 11, 12, 13, 23, 24, 14, 15, 25, 26, 16, 17, 40, 27, 41, 18, 30,
28, 31, 19, 29, 42, 32, 33, 43, 44, 34, 35, 60, 36, 50, 37, 45, 61, 46, 51,
47, 48, 38, 39, 49, 80, 52, 53, 81, 62, 54, 70, 55, 63, 82, 56, 57, 64, 71,
65, 66, 58, 59, 83, 84, 72, 90, 73, 85, 67, 68, 91, 69, 86, 74, 75, 87, 400,
76, 77, 401, 100, 78, 92, 93, 88, 94, 79, 89, 200, 201, 101
> The frequencies of occurrence of the 7 prime sums over the first 10000
> terms
are:
2 1788448
3 2318299
5 3624036
7 4340644
11 4100476
13 2246844
17 503513
suggesting non-uniformity of distribution.
Best regards,
Chris
----------------
>> Hello SeqFans,
a(n) is the smallest integer not yet present in S such that the leftmost
digit of a(n) and the rightmost digit of a(n-1) sum up to a prime -- with
a(1)=1.
S=1,2,3,4,7,6,5,8,9,20,21,10,22,11,12,13,23,24,14,15,25,26,16,...
(by hand)
I think S is a derangement of N.
Say a record of the successive "prime-sums" is kept [those sums can only be
equal to 2, 3, 5, 7, 11, 13 and 17]; will the fre- quency of each sum slowly
converge to 1/7th?
Best,
É.
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