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A377971 Square array of primes p >= 7, read by decreasing antidiagonals. Each row lists, in increasing order, the primes that share the same sum of their neighboring prime gaps.

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%I A377971 #26 Nov 17 2024 07:07:24
%S A377971 7,11,29,13,31,23,17,59,37,53,19,61,47,97,89,41,73,67,139,199,223,43,
%T A377971 137,79,149,359,251,113,71,151,83,157,367,337,127,331,101,179,131,173,
%U A377971 389,467,307,479,631,103,239,163,181,449,547,317,523,797,211,107,269,167,191,521,557,409,953,1087,293,1381
%N A377971 Square array of primes p >= 7, read by decreasing antidiagonals. Each row lists, in increasing order, the primes that share the same sum of their neighboring prime gaps.
%C A377971 First column is subset of A046931, which starts with 3. Here, 3 and 5 are omitted.
%C A377971 The related sum can be denoted Sum_prime_gaps, S = pg_inf + pg_sup.
%F A377971 Sum_prime_gaps_a(n) = S_a(n) = (A002260(n))*2 + 4.
%e A377971 Square array begins:
%e A377971 .
%e A377971 S = pg_inf + pg_sup |
%e A377971       2*(3..k)      |
%e A377971 -----------------------------------------------------------------------
%e A377971           6         |   7,  11,  13,  17,  19,  41,  43,  71, 101, ... A098414
%e A377971           8         |  29,  31,  59,  61,  73, 137, 151, 179, 239, ...
%e A377971          10         |  23,  37,  47,  67,  79,  83, 131, 163, 167, ...
%e A377971          12         |  53,  97, 139, 149, 157, 173, 181, 191, 241, ...
%e A377971          14         |  89, 199, 359, 367, 389, 449, 521, 619, 661, ...
%e A377971 .
%e A377971 31, 59 and 179 are in the same row because their preceding and succeeding prime gaps, (pg_inf, pg_sup), respectively (2,6), (6,2) and (6,2) each equally sum up to 8.
%e A377971 53 and 181 are in the same row because their preceding and succeeding prime gaps, (pg_inf, pg_sup), respectively (6,6) and (2,10) each equally sum up to 12. Here, 53 also happens to be a balanced prime as its corresponding gaps, (6,6), are equal.
%Y A377971 Cf. A000040, A001223, A098414, A002260, A006562.
%K A377971 nonn,tabl
%O A377971 1,1
%A A377971 _Tamas Sandor Nagy_, Nov 13 2024