A118859 Numbers k such that k-1, k+1, 2*k-1, 2*k+1, 3*k-1 and 3*k+1 are primes.

6, 53550, 420420, 422310, 1624350, 2130240, 3399900, 5199810, 5246010, 6549270, 7384440, 7775880, 9516570, 9565710, 10430280, 11845260, 13207950, 14562870, 14619990, 18747960, 20099940, 21596820, 21968100, 24358950, 24610740, 26916120, 28359240, 30838080

Offset: 1

Author

Labos Elemer, May 03 2006

Keywords

• nonn

Examples

			6 is a term because 5, 7, 11, 13, 17, 19 are all prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..4000

Crossrefs

Subsequence of A014574 and A066388.

Subsequences: A118860, A349321.

Cf. A014574, A290811, A348348.

Programs

Mathematica

Select[Range[25*10^6],AllTrue[Flatten[{#+{1,-1},2#+{1,-1},3#+{1,-1}}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 13 2016 *)

PARI

isok(k) = isprime(k-1) && isprime(k+1) && isprime(2*k-1) && isprime(2*k+1) && isprime(3*k-1) && isprime(3*k+1); \\ Amiram Eldar, Mar 13 2025

Formula

a(n) = 6*A290811(n).

Extensions

Edited by Don Reble, May 16 2006

a(26)-a(28) from Jon E. Schoenfield, Dec 07 2021