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A231609 Table whose n-th row consists of primes p such that p + 2n is the next prime, read by antidiagonals.

%I A231609 #20 Dec 15 2015 00:55:45
%S A231609 3,7,5,23,13,11,89,31,19,17,139,359,47,37,29,199,181,389,53,43,41,113,
%T A231609 211,241,401,61,67,59,1831,293,467,283,449,73,79,71,523,1933,317,509,
%U A231609 337,479,83,97,101,887,1069,2113,773,619,409,491,131,103,107
%N A231609 Table whose n-th row consists of primes p such that p + 2n is the next prime, read by antidiagonals.
%C A231609 The plot has an unusual gap near 10^5. Why?
%H A231609 T. D. Noe, <a href="/A231609/b231609.txt">Rows n = 1..100 of triangle, flattened</a>
%e A231609 The following sequences are read by antidiagonals
%e A231609 {   3,    5,   11,   17,   29,   41,   59,   71,  101,  107, ...}
%e A231609 {   7,   13,   19,   37,   43,   67,   79,   97,  103,  109, ...}
%e A231609 {  23,   31,   47,   53,   61,   73,   83,  131,  151,  157, ...}
%e A231609 {  89,  359,  389,  401,  449,  479,  491,  683,  701,  719, ...}
%e A231609 { 139,  181,  241,  283,  337,  409,  421,  547,  577,  631, ...}
%e A231609 { 199,  211,  467,  509,  619,  661,  797,  997, 1201, 1237, ...}
%e A231609 { 113,  293,  317,  773,  839,  863,  953, 1409, 1583, 1847, ...}
%e A231609 {1831, 1933, 2113, 2221, 2251, 2593, 2803, 3121, 3373, 3391, ...}
%e A231609 { 523, 1069, 1259, 1381, 1759, 1913, 2161, 2503, 2861, 3803, ...}
%e A231609 { 887, 1637, 3089, 3413, 3947, 5717, 5903, 5987, 6803, 7649, ...}
%e A231609 ...
%t A231609 nn = 10; t = Table[{}, {nn}]; complete = 0; lastP = 3; While[complete < nn, p = NextPrime[lastP]; diff = p - lastP; If[diff <= 2*nn && Length[t[[diff/2]]] < nn - diff/2 + 1, AppendTo[t[[diff/2]], lastP]; If[Length[t[[diff/2]]] == nn - diff/2 + 1, complete++]]; lastP = p]; t2 = PadRight[t, {nn, nn}, 0]; Table[t2[[n-j+1, j]], {n, nn}, {j, n}]
%Y A231609 Cf. A001359, A029710, A031924, A031926, A031928.
%Y A231609 Cf. A031930, A031932, A031934, A031936, A031938.
%Y A231609 Cf. A000230 (numbers in first column).
%K A231609 nonn,tabl,look
%O A231609 1,1
%A A231609 _T. D. Noe_, Nov 26 2013