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

[Eric Angelini]

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

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>> 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.