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) = 5.

a(1) = 4375 = (2^1)*(3^7)+1 = 5 * 5 * 5 * 5 * 7.

a(2) = 19684 = (2^0)*(3^9)+1 = 2 * 2 * 7 * 19 * 37.

a(3) = 7077889 = (2^18)*(3^3)+1 = 7 * 13 * 13 * 31 * 193 (prime factors each have all odd digits).

a(4) = 7962625 = (2^15)*(3^5)+1 = 5 * 5 * 5 * 11 * 5791 (again, coincidentally, prime factors each have all odd

digits).

a(7) = 129140164 = (2^0)*(3^17)+1 = 2 * 2 * 103 * 307 * 1021.

a(15) = 8589934593 = (2^33)*(3^0)+1 = 3 * 3 * 67 * 683 * 20857.

a(21) = 34359738369 = (2^35)*(3^0)+1 = 3 * 11 * 43 * 281 * 86171.

a(30) = 793437161473 = (2^11)*(3^18)+1 = 11 * 11 * 11 * 43 * 13863281.

a(32) = 847288609444 = (2^0)*(3^25)+1 = 2 * 2 * 61 * 151 * 22996651.

a(47) = 68630377364884 = (2^0)*(3^29)+1 = 2 * 2 * 523 * 6091 * 5385997.

a(48) = 70368744177665 = (2^46)*(3^0)+1 = 5 * 277 * 1013 * 1657 * 30269.

a(81) = 50031545098999708 = (2^0)*(3^35)+1 = 2 * 2 * 61 * 547 * 374857981681.

a(89) = 144115188075855873 = (2^57)*(3^0)+1 = 3 * 3 * 571 * 174763 * 160465489.

a(99) = 450283905890997364 = (2^0)*(3^37)+1 = 2 * 2 * 18427 * 107671 * 56737873.

a(113) = 4611686018427387905 = (2^62)*(3^0)+1 = 5 * 5581 * 8681 * 49477 * 384773.

Intersection of A014614 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.

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.

Sequence in context: A028511 A101558 A163583 this_sequence A027506 A152931 A045013

Adjacent sequences: A111342 A111343 A111344 this_sequence A111346 A111347 A111348

easy,nonn

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

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