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

1,3

Comments

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

Links

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

Formula

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

Example

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.

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 *)

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(valuation(s[i] - 1, 2), ", "))); } \\ Amiram Eldar, Sep 02 2024

Crossrefs

Cf. A005109, A007814, A374578.

Sequence in context: A132082 A129644 A081517 * A104778 A356184 A292477

Adjacent sequences: A374574 A374575 A374576 * A374578 A374579 A374580

Keyword

nonn

Author

William C. Laursen, Jul 11 2024

Extensions

More terms from Stefano Spezia, Jul 12 2024

Status

approved