A174099 Indices of primes of the form 2^t*3^u + 1 in the primes.

1, 2, 3, 4, 6, 7, 8, 12, 21, 25, 29, 38, 44, 55, 84, 93, 106, 136, 191, 211, 232, 378, 422, 483, 539, 1272, 1470, 2014, 2111, 4144, 5359, 6543, 13006, 13632, 18802, 28547, 39420, 51327, 59982, 62947, 66875, 78156, 91466, 113675, 132938, 148273, 193541

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 07 2010

Keywords

• nonn

Comments

Numbers k such that 2^t*3^u + 1 = prime(k).

Examples

			a(1) = 1 because 2^0 * 3^0 + 1 = 2 = prime(1).
a(2) = 2 because 2^1 * 3^0 + 1 = 3 = prime(2).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..166

Crossrefs

Cf. A000720, A005109.

Programs

Mathematica

With[{lim = 10^7}, PrimePi[Select[Sort@ Flatten@ Table[2^i * 3^j + 1, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}], PrimeQ]]] (* Amiram Eldar, Sep 02 2024 *)

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(primepi(s[i]), ", ")));} \\ Amiram Eldar, Sep 02 2024

Formula

a(n) = A000720(A005109(n)).

Extensions

Corrected and extended by Charles R Greathouse IV, Mar 21 2010