A367855 The slowest increasing sequence of semiprimes such that a(n-1) + a(n) is prime.

4, 9, 10, 21, 22, 25, 34, 39, 58, 69, 82, 85, 94, 129, 134, 143, 194, 203, 206, 213, 218, 221, 278, 291, 302, 305, 314, 327, 334, 339, 362, 365, 386, 411, 446, 473, 566, 597, 626, 633, 674, 687, 694, 745, 766, 793, 1018, 1081, 1126, 1141, 1198, 1219, 1402, 1417, 1486, 1513, 1654, 1689, 1718, 1731

Offset: 1

Author

Zak Seidov and Robert Israel, Dec 02 2023

Keywords

• nonn

Comments

a(2*n) is odd and a(2*n-1) is twice a prime where n is a positive integer. - David A. Corneth, Dec 03 2023

Examples

			a(4) = 21 because a(3) = 10, 21 = 3 * 7 is a semiprime > 10, 10 + 21 = 31 is prime, and no smaller semiprime > 10 works.
		

Links

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

Crossrefs

Cf. A001358, A116656, A126938.

Programs

Maple

R:= 4: s:= 4:
for count from 2 to 100 do
  for t from s+1 by 2 do
    if isprime(s+t) and numtheory:-bigomega(t) = 2 then
      R:= R,t; s:= t; break
    fi
  od
od:
R;

Mathematica

s = {q = 4}; Do[p = q + 1; While[ PrimeOmega[p] != 2, p = p + 2]; AppendTo[s, q = p], {120}]; s