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A268305 Numbers k such that k - 37, k - 1, k + 1, k + 37 are consecutive primes.

%I A268305 #30 Mar 04 2025 11:09:27
%S A268305 1524180,3264930,3970530,5438310,5642910,6764940,8176410,10040880,
%T A268305 10413900,10894320,11639520,12352980,13556340,15900720,16897590,
%U A268305 17283360,18168150,18209100,18686910,19340220,20099940,20359020,20483340,21028290,21846360
%N A268305 Numbers k such that k - 37, k - 1, k + 1, k + 37 are consecutive primes.
%C A268305 This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
%C A268305 The numbers k - 37 and k + 1 belong to A156104 (p and p + 36 are primes) and A134117 (p where p + 36 is the next prime).
%C A268305 The numbers k - 37 and k - 1 belong to A271347 (p and p + 38 are primes).
%H A268305 Karl V. Keller, Jr., <a href="/A268305/b268305.txt">Table of n, a(n) for n = 1..10000</a>
%H A268305 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A268305 1524180 is the average of the four consecutive primes 1524143, 1524179, 1524181, 1524217.
%e A268305 3264930 is the average of the four consecutive primes 3264893, 3264929, 3264931, 3264967.
%t A268305 Select[Partition[Prime[Range[14*10^5]],4,1],Differences[#]=={36,2,36}&][[All,2]]+1 (* _Harvey P. Dale_, Mar 12 2018 *)
%o A268305 (Python)
%o A268305 from sympy import isprime,prevprime,nextprime
%o A268305 for i in range(0,30000001,6):
%o A268305   if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-37 and nextprime(i+1) == i+37 : print (i,end=', ')
%Y A268305 Cf. A014574, A077800 (twin primes), A249674, A256753.
%K A268305 nonn
%O A268305 1,1
%A A268305 _Karl V. Keller, Jr._, Apr 17 2016