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

1,1

Comments

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

Links

Table of n, a(n) for n=1..22.

Example

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

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 *)

Crossrefs

Cf. A014574, A066388, A118859, A349321, A348348.

Sequence in context: A251998 A210389 A364435 * A186595 A210076 A184375

Adjacent sequences: A118857 A118858 A118859 * A118861 A118862 A118863

Keyword

nonn

Author

Labos Elemer, May 03 2006

Extensions

Edited by Don Reble, May 16 2006

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

Status

approved