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A271323 Numbers n such that n - 41, n - 1, n + 1, n + 41 are consecutive primes.

%I A271323 #32 Feb 16 2025 08:33:33
%S A271323 383220,1269642,1528938,2590770,3014700,3158298,3697362,3946338,
%T A271323 4017312,4045050,4545642,4711740,4851618,4871568,5141178,5194602,
%U A271323 5925042,5972958,5990820,6075030,6179862,6212202,6350760,6442938,6549312,6910638,6912132
%N A271323 Numbers n such that  n - 41, n - 1, n + 1, n + 41 are consecutive primes.
%C A271323 This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
%C A271323 The terms ending in 0 belong to A249674 (divisible by 30).
%C A271323 The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.
%C A271323 The numbers n - 40 and n + 1 belong to A126721 (p such that p + 40 is the next prime) and A271981 (p and p + 40 are primes).
%C A271323 The numbers n - 40 and n - 1 belong to A271982 (p and p + 42 are primes).
%H A271323 Karl V. Keller, Jr., <a href="/A271323/b271323.txt">Table of n, a(n) for n = 1..10000</a>
%H A271323 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A271323 383220 is the average of the four consecutive primes 383179, 383219, 383221, 383261.
%e A271323 1269642 is the average of the four consecutive primes 1269601, 1269641, 1269643, 1269683.
%t A271323 Mean/@Select[Partition[Prime[Range[472000]],4,1],Differences[#] == {40,2,40}&] (* _Harvey P. Dale_, Oct 16 2021 *)
%o A271323 (Python)
%o A271323 from sympy import isprime,prevprime,nextprime
%o A271323 for i in range(0,12000001,6):
%o A271323   if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-41 and nextprime(i+1) == i+41: print (i,end=', ')
%Y A271323 Cf. A014574, A077800 (twin primes), A249674, A256753.
%K A271323 nonn
%O A271323 1,1
%A A271323 _Karl V. Keller, Jr._, May 15 2016