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

1,2

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000720, A005109.

Sequence in context: A239011 A070525 A283112 * A099005 A336739 A257648

Adjacent sequences: A174096 A174097 A174098 * A174100 A174101 A174102

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 07 2010

Extensions

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

Status

approved