A364442 a(n) is the smallest number > a(n-1) such that a(n-1) + a(n) is a triprime (A014612), with a(1) = 1.

1, 7, 11, 16, 26, 37, 38, 40, 52, 53, 57, 59, 65, 73, 74, 79, 85, 86, 88, 94, 96, 99, 108, 114, 116, 120, 122, 123, 132, 134, 139, 140, 142, 143, 147, 163, 169, 174, 180, 183, 186, 188, 197, 202, 204, 206, 212, 213, 215, 219, 223, 229, 236, 238, 239, 244, 250, 256, 262, 268, 271, 277, 278, 283

Offset: 1

Author

Zak Seidov and Robert Israel, Jul 25 2023

Keywords

• nonn

Comments

For n > 1, a(n) is the least number > a(n-1) such that A001222(a(n) + a(n-1)) = 3.

a(n-1) + a(n) is the least triprime > 2*a(n-1).

Examples

			a(3) = 11 because a(2) = 7, none of 7 + 8 = 15, 7 + 9 = 16 and 7 + 10 = 17 is a triprime, but 7 + 11 = 18 = 2*3^2 is a triprime.
		

Links

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

Crossrefs

Cf. A001222, A014612, A073627, A263349, A357713.

Programs

Maple

R:= 1: x:= 1:
for i from 1 to 100 do
   for y from x+1 while numtheory:-bigomega(x+y) <> 3 do od:
   R:= R,y;
   x:= y
od:
R;

Mathematica

s = {p = 1}; Do[q = p + 1; While[3 != PrimeOmega[p + q],
q++];  AppendTo[s, p = q], {100}]; s