A360666 Semiprimes k such that k+4, k+6, k+9, k+10 and k+14 are also semiprimes.

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

Robert Israel, Table of n, a(n) for n = 1..9340

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

Adjacent sequences: A360663 A360664 A360665 * A360667 A360668 A360669

Keyword

nonn

Author

Zak Seidov and Robert Israel, Feb 15 2023

Status

approved