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%I #31 May 05 2022 15:08:17
%S 7,23,37,59,67,71,73,89,163,167,233,241,269,277,367,379,389,449,479,
%T 557,569,587,599,601,631,743,751,757,809,967,983,1009,1033,1039,1109,
%U 1117,1229,1283,1297,1307,1361,1439,1523,1559,1607,1609,1613,1637,1669
%N Primes prime(k) such that the gap prime(k-1) - prime(k-2) equals the gap prime(k+2) - prime(k+1).
%C This rephrases patterns of the form g, *, *, g in four successive entries of A001223, where * denotes arbitrary, not necessarily distinct, values.
%C The associated indices are n = 4, 9, 12, 17, 19, 20, 21, 24, 38, ...
%C Each entry is the second next prime after A022887(n). - _R. J. Mathar_, Jul 12 2013
%H Karl-Heinz Hofmann, <a href="/A227064/b227064.txt">Table of n, a(n) for n = 1..10000</a>
%F Prime(k) such that A001223(k-2) = A001223(k+1).
%e 7 is in the sequence since the gap between the previous two primes (3 and 5) is equal to the gap between the next two primes (11 and 13).
%o (Python) from sympy import sieve as p
%o print([p[k] for k in range(3, 264) if p[k-1] - p[k-2] == p[k+2] - p[k+1]])
%o # _Karl-Heinz Hofmann_, May 04 2022
%Y Cf. A001223, A022887.
%K nonn,less
%O 1,1
%A _Juri-Stepan Gerasimov_, Jun 30 2013
%E Corrected by _R. J. Mathar_, Jul 12 2013
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