This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%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