A374577 Pierpont primes are primes of the form 2^t*3^u + 1; this sequence gives the t's in order.

0, 1, 2, 1, 2, 4, 1, 2, 3, 5, 2, 1, 6, 8, 4, 1, 6, 8, 7, 4, 1, 5, 2, 7, 4, 7, 12, 3, 11, 1, 3, 16, 6, 14, 5, 12, 3, 5, 10, 18, 7, 12, 17, 11, 16, 13, 15, 8, 16, 4, 6, 19, 2, 20, 2, 18, 15, 1, 6, 22, 11, 21, 1, 13, 12, 11, 26, 25, 30, 19, 24, 20, 27, 16, 23, 11

Offset: 1

Author

William C. Laursen, Jul 11 2024

Keywords

• nonn

Comments

This sequence gives the exponents of 2's in the Pierpont primes, A374578 gives the exponents of 3's.

Examples

			a(1) = 0, because the first Pierpont prime is 2 = 2^0 * 3^0 + 1.
a(6) = 4, because the sixth Pierpont prime is 17 = 2^4 * 3^0 + 1.
a(7) = 1, because the seventh Pierpont prime is 19 = 2^1 * 3^2 + 1.
		

Links

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

Crossrefs

Cf. A005109, A007814, A374578.

Programs

Mathematica

With[{lim = 10^11}, IntegerExponent[Select[Sort@ Flatten@Table[2^i*3^j + 1, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}], PrimeQ] - 1, 2]] (* 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(valuation(s[i] - 1, 2), ", ")));} \\ Amiram Eldar, Sep 02 2024

Formula

a(n) = A007814(A005109(n)-1).

Extensions

More terms from Stefano Spezia, Jul 12 2024