A118860 Numbers k such that k-1, k+1, 2k-1, 2k+1, 3k-1, 3k+1, 4k-1 and 4k+1 are all primes.

21968100, 37674210, 81875220, 356467230, 416172330, 750662640, 1007393730, 1150070040, 1586271960, 1963954650, 3127171320, 3669568560, 4377895410, 4383541050, 5575083360, 5686935870, 5708418870, 7365234450, 7478474430, 7681046100, 8453862690, 8898688680

Offset: 1

Author

Labos Elemer, May 03 2006

Keywords

• nonn

Comments

All terms are multiples of 210, hence simpler code is possible.

Examples

			21968100 is a term because 21968099, 21968101, 43936199, 43936201, 65904299, 65904301, 87872399, 87872401 are all prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Subsequence of A014574, A066388 and A118859.

Subsequence: A349321.

Cf. A174293, A348348.

Programs

Mathematica

tb={};Do[If[(PrimeQ[n-1]&&PrimeQ[n+1])&& (PrimeQ[2*n-1]&&PrimeQ[2*n+1])&& (PrimeQ[3*n-1]&&PrimeQ[3*n+1])&& (PrimeQ[4*n-1]&&PrimeQ[4*n+1]), Print[n];AppendTo[tb,n]], {n,21968100,10^8,210}];tb
Select[210*Range[424*10^5],AllTrue[{#-1,#+1,2#-1,2#+1,3#-1,3#+1,4#-1,4#+1},PrimeQ]&] (* Harvey P. Dale, Jul 23 2024 *)

PARI

isok(k) = if(k % 210, 0, for(i = 1, 4, forstep(j = -1, 1, 2, if(!isprime(i*k-j), return(0)))); 1); \\ Amiram Eldar, Mar 13 2025

Formula

a(n) = 210*A174293(n).

Extensions

Edited by Don Reble, May 16 2006

a(20)-a(22) from Pontus von Brömssen, Oct 14 2021