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A265651 Numbers n such that n-29, n-1, n+1 and n+29 are consecutive primes.

%I A265651 #19 May 22 2025 10:21:44
%S A265651 14592,84348,151938,208962,241392,254490,397182,420192,494442,527700,
%T A265651 549978,581982,637200,641550,712602,729330,791628,850302,975552,
%U A265651 995052,1086558,1107852,1157670,1245450,1260798,1286148,1494510,1555290,1608912
%N A265651 Numbers n such that n-29, n-1, n+1 and n+29 are consecutive primes.
%C A265651 This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
%C A265651 The terms ending in 0 are divisible by 30 (cf. A249674).
%C A265651 The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.
%C A265651 The numbers n-29 and n+1 belong to A252090 (p and p+28 are primes) and A124595 (p where p+28 is the next prime).
%C A265651 The numbers n-29 and n-1 belong to A049481 (p and p+30 are primes).
%H A265651 Karl V. Keller, Jr., <a href="/A265651/b265651.txt">Table of n, a(n) for n = 1..10000</a>
%H A265651 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A265651 14592 is the average of the four consecutive primes 14563, 14591, 14593, 14621.
%e A265651 84348 is the average of the four consecutive primes 84319, 84347, 84349, 84377.
%t A265651 Select[Prime@Range@100000, NextPrime[#, {1, 2, 3}] == {28, 30, 58} + # &] + 29 (* _Vincenzo Librandi_, Dec 12 2015 *)
%t A265651 Mean/@Select[Partition[Prime[Range[125000]],4,1],Differences[#]=={28,2,28}&] (* _Harvey P. Dale_, May 02 2016 *)
%o A265651 (Python)
%o A265651 from sympy import isprime,prevprime,nextprime
%o A265651 for i in range(0,1000001,6):
%o A265651    if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-29 and nextprime(i+1) == i+29 :  print (i,end=', ')
%Y A265651 Cf. A014574, A077800 (twin primes), A249674, A256753.
%K A265651 nonn
%O A265651 1,1
%A A265651 _Karl V. Keller, Jr._, Dec 11 2015