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A257638 Numbers n such that n-25, n-1, n+1 and n+25 are consecutive primes.

%I A257638 #17 May 22 2025 10:21:43
%S A257638 232962,311712,431832,435948,473352,501342,525492,596118,635388,
%T A257638 665922,699792,754182,842448,1013502,1017648,1036002,1156848,1255452,
%U A257638 1284738,1306692,1479912,1516128,1551732,1560708,1595928,1659348,1690572,1745112
%N A257638 Numbers n such that n-25, n-1, n+1 and n+25 are consecutive primes.
%C A257638 This is a subsequence of A014574 (average of twin prime pairs) and A256753.
%C A257638 The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.
%C A257638 The numbers n-25 and n+1 belong to A033560 (p and p+24 are primes) and A098974 (p where p+24 is the next prime).
%C A257638 The numbers n-25 and n-1 belong to A252089 (p and p+26 are primes).
%H A257638 Karl V. Keller, Jr., <a href="/A257638/b257638.txt">Table of n, a(n) for n = 1..10000</a>
%H A257638 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A257638 232962 is the average of the four consecutive primes 232937, 232961, 232963, 232987.
%e A257638 311712 is the average of the four consecutive primes 311687, 311711, 311713, 311737.
%o A257638 (Python)
%o A257638 from sympy import isprime,prevprime,nextprime
%o A257638 for i in range(0,1000001,6):
%o A257638   if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-25 and nextprime(i+1) == i+25: print (i,end=', ')
%Y A257638 Cf. A014574, A077800 (twin primes), A249674, A256753.
%K A257638 nonn
%O A257638 1,1
%A A257638 _Karl V. Keller, Jr._, Nov 04 2015