A336772 Sums s of positive exponents such that no prime of the form 2^j*3^k + 1 with j + k = s exists.

12, 24, 33, 46, 48, 60, 72, 74, 80, 96, 102, 111, 118, 120, 130, 132, 141, 142, 144, 147, 159, 162, 165, 166, 168, 186, 200, 216, 234, 240, 242, 252, 258, 288, 306, 309, 312, 318, 358, 370, 374, 375, 384, 399, 405, 408, 414, 420, 432, 435, 462, 464, 468, 478

Offset: 1

Author

Hugo Pfoertner, based on a suggestion from Rainer Rosenthal, Aug 24 2020

Keywords

• nonn

Examples

			a(1) = 12, because none of the 11 numbers {2^1*3^11+1, 2^2*3^10+1, ..., 2^11*3^1+1} = {354295, 236197, 157465, 104977, 69985, 46657, 31105, 20737, 13825, 9217, 6145} is prime,
a(2) = 24: none of the 23 numbers {2^1*3^23+1, 2^2*3^22+1, ..., 2^23*3^1+1} = {188286357655, 125524238437, 83682825625, 55788550417, ..., 56623105, 37748737, 25165825} is prime.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A033845, A058383, A336773.

Programs

PARI

for(s=2,500, my(t=1); for(j=1,s-1, my(k=s-j); if(isprime(2^j*3^k+1),t=0;break)); if(t,print1(s,", ")))