A376701 The values of j in primes of the form 2^i*3^j - 1 (A005105) in the order of their appearance.

1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 2, 3, 0, 1, 1, 3, 4, 3, 5, 2, 4, 7, 1, 3, 0, 7, 8, 5, 6, 3, 5, 2, 0, 7, 4, 2, 9, 3, 10, 5, 0, 1, 5, 12, 9, 4, 7, 2, 13, 10, 15, 5, 6, 4, 13, 8, 17, 0, 15, 5, 12, 6, 13, 20, 3, 7, 9, 4, 5, 14, 1, 9, 16, 15, 17, 11, 23, 13, 10, 1, 7, 7, 3, 19, 16, 3

Offset: 1

Author

Amiram Eldar, Oct 02 2024

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005105, A007949, A374578, A376699, A376700.

Programs

Mathematica

With[{lim = 10^13}, IntegerExponent[Select[Sort@ Flatten@Table[2^i*3^j - 1, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}], PrimeQ] + 1, 3]]

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(valuation(s[i] + 1, 3), ", "))); }

Formula

a(n) = A007949(A005105(n)+1).