A271349 - OEIS

%I #14 Sep 16 2024 20:32:02

%S 276672,558828,1050852,1278288,1486908,1625418,2536308,2538918,

%T 2690958,2731242,3015162,3252678,3268338,3508278,3711612,4233708,

%U 4575912,4717962,5004402,5108352,5404032,5482782,5519082,5525328,5640918,5654358,5995818

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

%C This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.

%C The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.

%C 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 The numbers n - 35 and n - 1 belong to A156104 (p and p + 36 are primes).

%H Karl V. Keller, Jr., <a href="/A271349/b271349.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>

%e 276672 is the average of the four consecutive primes 276637, 276671, 276673, 276707.

%e 558828 is the average of the four consecutive primes 558793, 558827, 558829, 558863.

%t Select[Partition[Prime[Range[500000]],4,1],Differences[#]=={34,2,34}&] [[All, 2]]+1 (* _Harvey P. Dale_, Oct 11 2017 *)

%o (Python)

%o from sympy import isprime,prevprime,nextprime

%o for i in range(0,1000001,6):

%o   if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-35 and nextprime(i+1) == i+35 :  print (i,end=', ')

%Y Cf. A014574, A077800 (twin primes), A256753.

%K nonn

%O 1,1

%A _Karl V. Keller, Jr._, Apr 04 2016