A333721 Numbers k such that k + 1, 2k + 1, 3k + 1, 4k + 1, and 6k + 1 are all prime.

1530, 4260, 25410, 26040, 78540, 111720, 174990, 211050, 214830, 395430, 403260, 409290, 459690, 487830, 512820, 711120, 779790, 910560, 1023750, 1135950, 1280370, 1312350, 1451520, 1464810, 1487070, 1563510, 1623360, 1698060, 1824330, 1933680, 2006340, 2097480

Offset: 1

Author

Pedro Caceres, May 04 2020

Keywords

• nonn

Comments

All terms are multiples of 6.

All terms are multiples of 30. - Robert Israel, Jun 17 2020

Examples

			25410 is in the sequence because 25411, 50821, 76231, 101641, 152461 are all prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Pedro Caceres, 30 Ideas about Prime Numbers

Crossrefs

Cf. A006093, A005097, A024892, A087370, A005098, A005099, A024898, A024899.

Programs

Maple

select(t -> andmap(isprime, [t+1,2*t+1,3*t+1,4*t+1,6*t+1]), [seq(i,i=30..3*10^6,30)]); # Robert Israel, Jun 17 2020

PARI

isok(m)={for(i=1, 6, if(i<>5&&!isprime(i*m+1), return(0))); 1}
{ forstep(n=0, 3*10^6, 6, if(isok(n), print1(n, ", "))) } \\ Andrew Howroyd, May 04 2020