A374578 - OEIS

A374578

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

0, 0, 0, 1, 1, 0, 2, 2, 2, 1, 3, 4, 1, 0, 3, 5, 2, 1, 2, 4, 6, 4, 6, 3, 5, 4, 1, 7, 2, 9, 8, 0, 7, 2, 8, 4, 10, 9, 6, 1, 8, 5, 2, 6, 3, 5, 4, 9, 4, 12, 11, 3, 14, 3, 15, 5, 7, 16, 13, 3, 10, 4, 17, 10, 11, 12, 3, 4, 1, 8, 5, 8, 4, 11, 7, 15, 12, 2, 10, 1, 22, 4

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OFFSET

1,7

COMMENTS

This sequence gives the exponents of 3's in the Pierpont primes, A374577 gives the exponents of 2's.

LINKS

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

FORMULA

a(n) = A007949(A005109(n)-1).

EXAMPLE

a(1) = 0, because the first Pierpont prime is 2 = 2^0 * 3^0 + 1.

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

a(7) = 2, because the seventh Pierpont prime is 19 = 2^1 * 3^2 + 1.

MATHEMATICA

With[{lim = 10^12}, IntegerExponent[Select[Sort@ Flatten@Table[2^i*3^j + 1, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}], PrimeQ] - 1, 3]] (* 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, 3), ", "))); } \\ Amiram Eldar, Sep 02 2024

CROSSREFS

Cf. A005109, A007949, A374577.

Sequence in context: A017125 A063276 A352682 * A361639 A055253 A103626

Adjacent sequences: A374575 A374576 A374577 * A374579 A374580 A374581

KEYWORD

nonn

AUTHOR

William C. Laursen, Jul 11 2024

EXTENSIONS

More terms from Stefano Spezia, Jul 12 2024

STATUS

approved