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

1,1

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.

Links

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

Example

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.

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)]);

Crossrefs

Cf. A014612.

Sequence in context: A344940 A344941 A334005 * A251987 A205662 A205951

Adjacent sequences: A367838 A367839 A367840 * A367842 A367843 A367844

Keyword

nonn

Author

Zak Seidov and Robert Israel, Dec 31 2023

Status

approved