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 A271349 Numbers n such that n - 35, n - 1, n + 1 and n + 35 are consecutive primes. 1
 276672, 558828, 1050852, 1278288, 1486908, 1625418, 2536308, 2538918, 2690958, 2731242, 3015162, 3252678, 3268338, 3508278, 3711612, 4233708, 4575912, 4717962, 5004402, 5108352, 5404032, 5482782, 5519082, 5525328, 5640918, 5654358, 5995818 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753. The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30. 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). The numbers n - 35 and n - 1 belong to A156104 (p and p + 36 are primes). LINKS Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Twin Primes EXAMPLE 276672 is the average of the four consecutive primes 276637, 276671, 276673, 276707. 558828 is the average of the four consecutive primes 558793, 558827, 558829, 558863. MATHEMATICA Select[Partition[Prime[Range[500000]], 4, 1], Differences[#]=={34, 2, 34}&] [[All, 2]]+1 (* Harvey P. Dale, Oct 11 2017 *) PROG (Python) from sympy import isprime, prevprime, nextprime for i in range(0, 1000001, 6): ..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-35 and nextprime(i+1) == i+35 :  print (i, end=', ') CROSSREFS Cf. A014574, A077800 (twin primes), A256753. Sequence in context: A069372 A157839 A237808 * A295472 A162765 A186879 Adjacent sequences:  A271346 A271347 A271348 * A271350 A271351 A271352 KEYWORD nonn AUTHOR Karl V. Keller, Jr., Apr 04 2016 STATUS approved

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Last modified January 20 21:49 EST 2021. Contains 340332 sequences. (Running on oeis4.)