A365240 Numbers k such that k + 4, k + 6, k + 9, k + 10, and k + 14 are all semiprimes, where 4, 6, 9, 10, 14 are the first 5 semiprimes.

0, 2113, 2185, 2557, 2977, 3089, 5357, 6397, 7057, 8017, 10537, 11549, 12049, 15697, 15829, 16729, 17597, 17633, 18637, 20485, 21949, 22417, 23257, 30017, 31357, 32857, 33509, 33949, 36749, 37909, 38053, 38509, 44137, 46033, 47189, 49345, 51073, 52333, 54173, 58645, 58813, 59317, 59425, 62237

Offset

1,2

Comments

It wouldn't work for the first 6 semiprimes: for any k, at least one of k + 4, k + 6, k + 9, k + 10, k + 14, and k + 15 is divisible by 4, and thus not a semiprime if k >= 1.

For n > 1, a(n) == 1 (mod 4).

Links

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

Example

a(3) = 2185 is a term because 2185 + 4 = 2189 = 11 * 199, 2185 + 6 = 2191 = 7 * 313, 2185 + 9 = 2194 = 2 * 1097, 2185 + 10 = 2195 = 5 * 439 and 2185 + 14 = 2199 = 3 * 733 are all semiprimes.

Maple

SP:= select(t -> numtheory:-bigomega(t) = 2, {$1..10^5}):
select(t -> {4, 6, 9, 10, 14} +~ t subset SP, [0, seq(i, i=1..10^5-14, 4)]);

Crossrefs

Cf. A001358.

Sequence in context: A107528 A246808 A217439 * A067632 A236446 A077731

Adjacent sequences: A365237 A365238 A365239 * A365241 A365242 A365243

Keyword

nonn

Author

Zak Seidov and Robert Israel, Aug 27 2023

Status

approved