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%I #16 Aug 28 2020 08:25:17
%S 12,24,33,46,48,60,72,74,80,96,102,111,118,120,130,132,141,142,144,
%T 147,159,162,165,166,168,186,200,216,234,240,242,252,258,288,306,309,
%U 312,318,358,370,374,375,384,399,405,408,414,420,432,435,462,464,468,478
%N Sums s of positive exponents such that no prime of the form 2^j*3^k + 1 with j + k = s exists.
%H Hugo Pfoertner, <a href="/A336772/b336772.txt">Table of n, a(n) for n = 1..500</a>
%e 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,
%e 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.
%o (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,", ")))
%Y Cf. A033845, A058383, A336773.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, based on a suggestion from _Rainer Rosenthal_, Aug 24 2020