login
A360666
Semiprimes k such that k+4, k+6, k+9, k+10 and k+14 are also semiprimes.
1
2977, 5357, 10537, 15697, 15829, 21949, 22417, 23257, 30017, 33509, 33949, 37909, 38509, 46033, 51073, 52333, 58813, 59317, 63937, 68617, 68797, 78409, 84877, 85273, 92513, 94177, 97229, 98233, 100873, 114977, 115697, 118177, 124229, 131977, 137257, 145217, 148637, 153973, 154549, 156193, 159253
OFFSET
1,1
COMMENTS
4, 6, 9, 10, 14 are the first five semiprimes.
The sixth semiprime is 15, but there are no semiprimes k such that k+4, k+9, k+10, k+14 and k+15 are all semiprimes, because at least one of k, k+4, k+9, k+10, k+14 and k+15 is divisible by 4, and 4 is the only semiprime divisible by 4.
All terms == 1, 25 or 29 (mod 36).
LINKS
EXAMPLE
a(3) = 10537 is a term because
10537 = 41 * 257
10537 + 4 = 10541 = 83 * 127
10537 + 6 = 10543 = 13 * 811
10537 + 9 = 10546 = 2 * 5273
10537 + 10 = 10547 = 53 * 199
10537 + 14 = 10551 = 3 * 3517
are all semiprimes.
MAPLE
select(t -> isprime((t+9)/2) and numtheory:-bigomega(t) = 2 and numtheory:-bigomega(t+4) = 2 and numtheory:-bigomega(t+6) = 2 and numtheory:-bigomega(t+10) = 2 and numtheory:-bigomega(t+14) = 2, [seq(seq(36*i+j, j=[1, 25, 29]), i=0..10^5)]);
CROSSREFS
Cf. A001358.
Sequence in context: A236140 A281330 A289455 * A202775 A235744 A235503
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Feb 15 2023
STATUS
approved