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A260959 Numbers n such that n is the average of four consecutive primes n-13, n-1, n+1 and n+13.

%I A260959 #12 May 22 2025 10:21:43
%S A260959 7950,10500,32970,33330,34470,36900,43050,66360,71550,74610,87120,
%T A260959 89070,92400,94560,95190,102000,104310,121950,125790,133980,148470,
%U A260959 156900,160710,168630,174930,182640,194070,204600,206250,230340,244380,246510
%N A260959 Numbers n such that n is the average of four consecutive primes n-13, n-1, n+1 and n+13.
%C A260959 This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).
%H A260959 Karl V. Keller, Jr., <a href="/A260959/b260959.txt">Table of n, a(n) for n = 1..10000</a>
%H A260959 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A260959 7950 is the average of the four consecutive primes 7937, 7949, 7951, 7963.
%e A260959 10500 is the average of the four consecutive primes 10487, 10499, 10501, 10513.
%o A260959 (Python)
%o A260959 from sympy import isprime,prevprime,nextprime
%o A260959 for i in range(0,300001,2):
%o A260959    if isprime(i-1) and isprime(i+1):
%o A260959     if prevprime(i-1) == i-13 and nextprime(i+1) == i+13 :  print (i,end=', ')
%o A260959 (Perl) use ntheory ":all"; say join ", ", map { $_+1 } grep { next_prime($_+2)-$_==14 } grep { $_-prev_prime($_)==12 } @{twin_primes(1e6)}; # _Dana Jacobsen_, Oct 03 2015
%Y A260959 Cf. A014574, A077800 (twin primes), A249674, A256753.
%K A260959 nonn
%O A260959 1,1
%A A260959 _Karl V. Keller, Jr._, Aug 06 2015