1,1

Eric Weisstein's World of Mathematics, Pierpont Prime

Eric Weisstein's World of Mathematics, Almost Prime

a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 4.

a(1) = 513 = (2^9)*(3^0)+1 = 3 * 3 * 3 * 19.

a(2) = 13825 = (2^9)*(3^3)+1 = 5 * 5 * 7 * 79.

a(3) = 32769 = (2^15)*(3^0)+1 = 3 * 3 * 11 * 331.

a(4) = 59050 = (2^0)*(3^10)+1 = 2 * 5 * 5 * 1181.

a(10) = 279937 = (2^7)*(3^7)+1 = 7 * 7 * 29 * 197 (lots of sevens).

a(24) = 33554433 = (2^25)*(3^0) = 3 * 11 * 251 * 4051.

a(60) = 31381059610 = (2^0)*(3^22)+1 = 2 * 5 * 5501 * 570461.

a(168) = 16677181699666570 = (2^0)*(3^34)+1 = 2 * 5 * 956353 * 1743831169.

Intersection of A014613 and A055600.

A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.

A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.

A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.

A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.

A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.

A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.

A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.

A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1.

Adjacent sequences: A111341 A111342 A111343 this_sequence A111345 A111346 A111347

Sequence in context: A060947 A066697 A076338 this_sequence A017681 A013957 A036087

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 08 2005

Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 08 2005