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 A096707 #8 Nov 29 2023 16:38:08
%S A096707 53,607,977,1289,2083,2351,4013,5563,8803,10657,11117,12583,14747,
%T A096707 16433,18731,22067,22699,28477,32833,39227,39749,41957,44357,46229,
%U A096707 46643,50053,50123,51869,53617,54469,56167,63377,63527,66797,74729,75217,76597,77023,93997
%N A096707 Balanced primes (A090403) of index 3.
%H A096707 Robert Price, <a href="/A096707/b096707.txt">Table of n, a(n) for n = 1..85</a>
%e A096707 607 is a member because 607 = (601 + 607 + 613)/3 =
%e A096707 (593 + 599 + 601 + 607 + 613 + 617 + 619)/7 = (401 + ... + 607 + ... + 823)/65.
%t A096707 f[n_] := Block[{c = 0, k = 1, p = Prime[n], s = Plus @@ Table[ Prime[i], {i, n - 1, n + 1}]}, While[k != n - 1, If[s == (2k + 1)p, c++ ]; k++; s = s + Prime[n - k] + Prime[n + k]]; c]; Prime[ Select[ Range[2, 250], f[ # ] == 3 &]]
%Y A096707 Cf. A096693, A096695, A096705, A096706, A096708, A096709.
%K A096707 nonn
%O A096707 1,1
%A A096707 _Robert G. Wilson v_, Jun 28 2004
%E A096707 a(37)-a(39) from _Robert Price_, Nov 29 2023