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

KEYWORD

nonn

AUTHOR

Zak Seidov and Robert Israel, Aug 27 2023

STATUS

approved