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) = 6.

a(1) = 14348908 = (2^0)*(3^15)+1 = 2 * 2 * 7 * 31 * 61 * 271.

a(2) = 134217729 = (2^27)*(3^0)+1 = 3 * 3 * 3 * 3 * 19 * 87211.

a(3) = 1073741825 = (2^30)*(3^0)+1 = 5 * 5 * 13 * 41 * 61 * 1321.

a(4) = 139314069505 = (2^18)*(3^12)+1 = 5 * 13 * 17 * 61 * 337 * 6133.

a(100) = 151115727451828646838273 = (2^77)*(3^0)+1 = 3 * 43 * 617 * 683 * 78233 * 35532364099.

a(127) = 9671406556917033397649409 = (2^83)*(3^0)+1 = 3 * 499 * 1163 * 2657 * 155377 * 13455809771.

a(153) = 523347633027360537213511522 = (2^0)*(3^56)+1 = 2 * 17 * 113 * 193 * 19489 * 36214795668330833.

a(169) = 2475880078570760549798248449 = (2^91)*(3^0)+1 = 3 * 43 * 2731 * 224771 * 1210483 * 25829691707.

Intersection of A046306 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.

A111344 gives the Pierpont 4-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.

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.

Sequence in context: A092378 A034634 A014497 this_sequence A136608 A015364 A081640

Adjacent sequences: A111343 A111344 A111345 this_sequence A111347 A111348 A111349

easy,nonn

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

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