A113434 -id:A113434 - cp's OEIS frontend

A113432 Pierpont semiprimes: semiprimes of the form (2^K)*(3^L)+1.

4, 9, 10, 25, 33, 49, 55, 65, 82, 129, 145, 217, 289, 649, 865, 973, 1537, 1945, 2049, 2305, 3073, 4097, 4609, 5833, 6145, 6913, 8193, 8749, 9217, 11665, 13123, 15553, 20737, 23329, 24577, 27649, 31105, 34993, 41473, 62209, 69985, 73729, 78733

Offset: 1

Jonathan Vos Post, Nov 01 2005

			a(1) = 4 = (2^0)*(3^1)+1 = 2^2 hence the semiprime A001358(1).
a(2) = 9 = (2^3)*(3^0)+1 = 3^2 hence the semiprime A001358(3).
a(3) = 10 = (2^0)*(3^2)+1 = 2 * 5 hence the semiprime A001358(4).
a(4) = 25 = (2^3)*(3^1)+1 = 5^2 hence the semiprime A001358(9).
a(5) = 33 = (2^5)*(3^0)+1 = 3 * 11 hence the semiprime A001358(11).
a(6) = 49 = (2^4)*(3^1)+1 = 7^2 hence the semiprime A001358(17).
a(7) = 55 = (2^1)*(3^3)+1 = 5 * 11 hence the semiprime A001358(19).

Vincenzo Librandi, Table of n, a(n) for n = 1..89
Chris Caldwell, "Pierpont primes." primeform posting, Oct 25, 2005.
Chris Caldwell, "Pierpont primes." primeform posting, Oct 25, 2005. [Cached copy]
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Semiprime

Cf. A001358, A003586, A005109, A055600, A111153, A111206, A113433, A113434.

Select[Range[10^5], Plus @@ Last /@ FactorInteger[ # ] == 2 && Max @@ First /@ FactorInteger[ # - 1] < 5 &] (* Ray Chandler, Jan 24 2006 *)

{a(n)} = Intersection of {(2^K)*(3^L)+1} A055600 and semiprimes A001358. a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 2.

A113433 Semi-Pierpont semiprimes: products of exactly two Pierpont primes A005109.

Original entry on oeis.org

4, 6, 9, 10, 14, 15, 21, 25, 26, 34, 35, 38, 39, 49, 51, 57, 65, 74, 85, 91, 95, 111, 119, 133, 146, 169, 185, 194, 218, 219, 221, 247, 259, 289, 291, 323, 326, 327, 361, 365, 386, 481, 485, 489, 511, 514, 545, 579, 629, 679, 703, 763, 771, 815, 866, 949, 965

Offset: 1

Jonathan Vos Post, Nov 01 2005

Semiprime both of whose prime factors are Pierpont primes (A005109), which are primes of the form (2^K)*(3^L)+1. Not to be confused with A113432: Pierpont semiprimes [Semiprimes of the form (2^K)*(3^L)+1]. This terminology itself is by analogy to what Tomaszewski used for the Sophie Germain counterparts A111153 and A111206.

			a(1) = 4 = 2^2 = [(2^0)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(1)*A005109(1).
a(2) = 6 = 2*3 = [(2^0)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(1)*A005109(2).
a(3) = 9 = 3^2 = [(2^1)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(2)*A005109(2).
a(4) = 10 = 2*5 = [(2^0)*(3^0)+1]*[(2^2)*(3^0)+1] = A005109(1)*A005109(3).
a(5) = 14 = 2*7 = [(2^0)*(3^0)+1]*[(2^1)*(3^1)+1] = A005109(1)*A005109(4).
a(6) = 15 = 3*5 = [(2^1)*(3^0)+1]*[(2^2)*(3^0)+1] = A005109(2)*A005109(3).

Vincenzo Librandi, Table of n, a(n) for n = 1..498
Chris Caldwell, "Pierpont primes." primeform posting, Oct 25, 2005.
Chris Caldwell, "Pierpont primes." primeform posting, Oct 25, 2005. [Cached copy]
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Semiprime

Cf. A001358, A003586, A005109, A055600, A111153, A111206, A113432, A113434.

Select[Range[10^3], Plus @@ Last /@ FactorInteger[ # ] == 2 && And @@ (Max @@ First /@ FactorInteger[ # - 1] < 5 &) /@ First /@ FactorInteger[ # ] &] (* Ray Chandler, Jan 24 2006 *)

{a(n)} = Semiprimes A001358 both of whose factors are of the form (2^K)*(3^L)+1. {a(n)} = {A005109(i)*A005109(j) for integers i and j not necessarily distinct}.

cp's OEIS Frontend

A113432 Pierpont semiprimes: semiprimes of the form (2^K)*(3^L)+1.

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