%I #7 Oct 02 2024 12:36:16
%S 3,4,5,6,8,10,11,13,15,16,18,21,22,25,31,32,36,39,40,42,51,57,61,63,
%T 65,66,71,73,79,82,94,97,106,107,110,120,121,127,128,129,130,138,142,
%U 144,161,192,204,205,212,216,232,234,244,259,264,265,308,329,346,348
%N Positions of primes in the sequence of numbers of the form 2^i * 3^j - 1 (A069353).
%H Amiram Eldar, <a href="/A376699/b376699.txt">Table of n, a(n) for n = 1..10000</a>
%F A069353(a(n)) = A003586(a(n)) - 1 = A005105(n).
%t With[{lim = 10^10}, Position[Sort@ Flatten@ Table[2^i*3^j - 1, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}], _?PrimeQ] // Flatten]
%o (PARI) lista(lim) = {my(s = List()); for(i = 0, logint(lim, 2), for(j = 0, logint(lim >> i, 3), listput(s, 2^i * 3^j - 1))); s = Set(s); for(i = 1, #s, if(isprime(s[i]), print1(i, ", ")));}
%Y Cf. A003586, A005105, A069353, A375906, A376700, A376701.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 02 2024