A383469 Semiprimes k such that A001358(k) + k and A001358(k) - k are also semiprimes.

4, 6, 46, 55, 87, 93, 94, 206, 298, 326, 362, 382, 394, 542, 562, 629, 758, 841, 866, 926, 993, 1046, 1079, 1147, 1167, 1234, 1317, 1469, 1477, 1561, 1774, 1895, 2047, 2227, 2245, 2515, 2638, 2705, 2894, 2902, 3007, 3031, 3063, 3202, 3269, 3409, 3453, 3466, 3487, 3809, 3891, 4058, 4174, 4207

Offset: 1

Author

Zak Seidov and Robert Israel, Apr 27 2025

Keywords

• nonn

Examples

			a(3) = 46 is a term because 46 = 2 * 23 is a semiprime, A001358(46) = 141, and 141 - 46 = 95 = 5 * 19 and 141 + 46 = 187 = 11 * 17 are semiprimes.
		

Links

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

Crossrefs

Cf. A001358, A383468.

Programs

Maple

k:= 0: K:= NULL: count:= 0:
for s from 1 while count < 100 do
  if numtheory:-bigomega(s) = 2 then
    k:= k+1;
    if andmap(t -> numtheory:-bigomega(t) = 2, [k, s-k, s+k]) then
      K:= K, k; count:= count+1;
    fi
  fi;
od:
K;

Formula

A001358(a(k)) = A383468(k).