[seqfan] Re: More stupid thingies with commas, sums & primes

Christopher Hunt gribble cgribble263 at btinternet.com
Wed Oct 19 14:33:57 CEST 2011


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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