A367841 Numbers k such that k, k + 2, k + 4, k + 6, k + 8, k + 10, and k + 12 are all triprimes (A014612).

151401, 151403, 151405, 151407, 179535, 201085, 247349, 248411, 250933, 250935, 292407, 298433, 322215, 379761, 441327, 482691, 482693, 499907, 508671, 517427, 584219, 584221, 586257, 586259, 605207, 705055, 705057, 705059, 718193, 726563, 727639, 728815, 812601, 814247, 814249, 814251, 831385

Offset: 1

Author

Zak Seidov and Robert Israel, Dec 31 2023

Keywords

• nonn

Comments

All terms are odd, because if k is even, at least one of k, k + 2, k + 4 and k + 6 is divisible by 8.

In the case of a(1) = 151401, k + 14, k + 16 and k + 18 are also triprimes.

In the case of a(143) = 2560187, k + 14, k + 16, k + 18 and k + 20 are also triprimes.

Examples

			a(5) = 179535 is a term because
179535 = 3 * 5 * 11969
179535 + 2 = 179537 = 17 * 59 * 179
179535 + 4 = 179539 = 29 * 41 * 151
179535 + 6 = 179541 = 3 * 3 * 19949
179535 + 8 = 179543 = 7 * 13 * 1973
179535 + 10 = 179545 = 5 * 149 * 241
179535 + 12 = 179547 = 3 * 97 * 617
are all triprimes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014612.

Programs

Maple

filter:= (t -> andmap(x -> numtheory:-bigomega(x)=3, [t,t+2,t+4,t+6,t+8,
t+10,t+12])):
select(filter, [seq(i,i=1 .. 10^6, 2)]);