A271323 - OEIS

%I #32 Feb 16 2025 08:33:33

%S 383220,1269642,1528938,2590770,3014700,3158298,3697362,3946338,

%T 4017312,4045050,4545642,4711740,4851618,4871568,5141178,5194602,

%U 5925042,5972958,5990820,6075030,6179862,6212202,6350760,6442938,6549312,6910638,6912132

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

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

%C The terms ending in 0 belong to A249674 (divisible by 30).

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

%C 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 The numbers n - 40 and n - 1 belong to A271982 (p and p + 42 are primes).

%H Karl V. Keller, Jr., <a href="/A271323/b271323.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 383220 is the average of the four consecutive primes 383179, 383219, 383221, 383261.

%e 1269642 is the average of the four consecutive primes 1269601, 1269641, 1269643, 1269683.

%t Mean/@Select[Partition[Prime[Range[472000]],4,1],Differences[#] == {40,2,40}&] (* _Harvey P. Dale_, Oct 16 2021 *)

%o (Python)

%o from sympy import isprime,prevprime,nextprime

%o for i in range(0,12000001,6):

%o   if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-41 and nextprime(i+1) == i+41: print (i,end=', ')

%Y Cf. A014574, A077800 (twin primes), A249674, A256753.

%K nonn,changed

%O 1,1

%A _Karl V. Keller, Jr._, May 15 2016