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 A274042 #22 Feb 16 2025 08:33:36
%S A274042 9401700,64312710,78563130,83494350,92978310,101520540,111105090,
%T A274042 121631580,136765860,138330780,139027950,145673850,157008390,
%U A274042 163050090,166418280,169288530,170473410,177920850,198963210,200765250,213504870,220428600
%N A274042 Numbers k such that k - 53, k - 1, k + 1, k + 53 are consecutive primes.
%C A274042 This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
%C A274042 The numbers n - 53 and n + 1 belong to A204665 (p such that p + 52 is the next prime).
%C A274042 The numbers n - 53 and n - 1 belong to primes p such that p + 54 is prime.
%H A274042 Karl V. Keller, Jr., <a href="/A274042/b274042.txt">Table of n, a(n) for n = 1..10000</a>
%H A274042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A274042 9401700 is the average of the four consecutive primes 9401647, 9401699, 9401701, 9401753.
%e A274042 64312710 is the average of the four consecutive primes 64312657, 64312709, 64312711, 64312763.
%t A274042 Select[Partition[Prime[Range[122*10^5]],4,1],Differences[#]=={52,2,52}&][[All,2]]+1 (* _Harvey P. Dale_, Mar 07 2018 *)
%o A274042 (Python)
%o A274042 from sympy import isprime,prevprime,nextprime
%o A274042 for i in range(0,250000001,6):
%o A274042 if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-53 and nextprime(i+1) == i+53: print (i,end=', ')
%Y A274042 Cf. A014574, A077800 (twin primes), A249674, A256753.
%K A274042 nonn
%O A274042 1,1
%A A274042 _Karl V. Keller, Jr._, Jun 07 2016