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A271349 Numbers n such that n - 35, n - 1, n + 1 and n + 35 are consecutive primes.

%I A271349 #15 Feb 16 2025 08:33:33
%S A271349 276672,558828,1050852,1278288,1486908,1625418,2536308,2538918,
%T A271349 2690958,2731242,3015162,3252678,3268338,3508278,3711612,4233708,
%U A271349 4575912,4717962,5004402,5108352,5404032,5482782,5519082,5525328,5640918,5654358,5995818
%N A271349 Numbers n such that n - 35, n - 1, n + 1 and n + 35 are consecutive primes.
%C A271349 This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
%C A271349 The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.
%C A271349 The numbers n - 35 and n + 1 belong to A252091 (p and p + 34 are primes) and A134116 (p such that p + 34 is the next prime).
%C A271349 The numbers n - 35 and n - 1 belong to A156104 (p and p + 36 are primes).
%H A271349 Karl V. Keller, Jr., <a href="/A271349/b271349.txt">Table of n, a(n) for n = 1..10000</a>
%H A271349 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A271349 276672 is the average of the four consecutive primes 276637, 276671, 276673, 276707.
%e A271349 558828 is the average of the four consecutive primes 558793, 558827, 558829, 558863.
%t A271349 Select[Partition[Prime[Range[500000]],4,1],Differences[#]=={34,2,34}&] [[All, 2]]+1 (* _Harvey P. Dale_, Oct 11 2017 *)
%o A271349 (Python)
%o A271349 from sympy import isprime,prevprime,nextprime
%o A271349 for i in range(0,1000001,6):
%o A271349   if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-35 and nextprime(i+1) == i+35 :  print (i,end=', ')
%Y A271349 Cf. A014574, A077800 (twin primes), A256753.
%K A271349 nonn
%O A271349 1,1
%A A271349 _Karl V. Keller, Jr._, Apr 04 2016