A128467 -id:A128467 - cp's OEIS frontend

A252862 Initial members of prime sextuples (n, n+2, n+6, n+8, n+18, n+20).

11, 18041, 97841, 165701, 392261, 663581, 1002341, 1068701, 1155611, 1329701, 1592861, 1678751, 1718861, 1748471, 2159231, 2168651, 2177501, 2458661, 2596661, 3215741, 3295541, 3416051, 3919241, 4353311, 5168921, 5201291, 5205461, 6404771

Offset: 1

Karl V. Keller, Jr., Dec 23 2014

nonn

This sequence is prime n, where there exist three twin prime pairs of (n,n+2), (n+6,n+8) and (n+18,n+20).
This is a subsequence of A132232 (Primes congruent to 11 mod 30 ).
Also, this is a subsequence of A128467 (30k+11).

			For n = 18041, the numbers, 18041, 18043, 18047, 18049, 18059, 18061, are primes.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes
Wikipedia, Twin prime

Cf. A077800 (twin primes), A030430 (primes,10*n+1), A132232, A128467, A172456.

Select[Prime[Range[2500]], Union[PrimeQ[{#, # + 2, # + 6, # + 8, # + 18, # + 20}]] = {True} &] (* Alonso del Arte, Dec 23 2014 *)
Select[Prime[Range[450000]],AllTrue[#+{2,6,8,18,20},PrimeQ]&] (* Harvey P. Dale, Jun 11 2023 *)

forprime(p=1,10^7,if(isprime(p+2) && isprime(p+6) && isprime(p+8) && isprime(p+18) && isprime(p+20), print1(p,", "))) \\ Derek Orr, Dec 31 2014

from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+6) and isprime(n+8) and isprime(n+18) and isprime(n+20): print(n,end=', ')

A382970 Numbers k such that {k, k+2, k+6, k+8, k+90, k+92, k+96, k+98} are all prime.

Original entry on oeis.org

11, 101, 15641, 3512981, 6655541, 20769311, 26919791, 41487071, 71541641, 160471601, 189425981, 236531921, 338030591, 409952351, 423685721, 431343461, 518137091, 543062621, 588273221, 637272191, 639387311, 647851571, 705497951, 726391571, 843404201, 895161341, 958438751, 960813851, 964812461, 985123961

Offset: 1

David Mellinger, Apr 10 2025

nonn

Each term is the initial member of two prime quadruples (A007530) with a difference of 90, the second-smallest possible distance between prime quadruples (A059925 has the smallest).

			a(1) corresponds to the set of primes {11,13,17,19,101,103,107,109} and a(2) corresponds to {101,103,107,109,191,193,197,199}.

Subsequence of A128467.

Cf. A007530, A059925.

find(corr([1 1 0 1 1 zeros(1,40) 1 1 0 1 1],isprime(3:2:1e8))>7.5)*2-97

a(n) == 11 (mod 30).

cp's OEIS Frontend

A252862 Initial members of prime sextuples (n, n+2, n+6, n+8, n+18, n+20).

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