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A113739 Pierpont 7-almost primes. 7-almost primes of form (2^K)*(3^L)+1. 7
339738625, 10460353204, 83682825625, 669462604993, 2641807540225, 3761479876609, 7625597484988, 18075490334785, 35184372088833, 481469424205825, 488038239039169, 570630428688385, 1125899906842625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..716

Eric Weisstein's World of Mathematics, Pierpont Prime

Eric Weisstein's World of Mathematics, Almost Prime

FORMULA

a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 7.

EXAMPLE

a(1) = 339738625 = (2^22)*(3^4)+1 = 5 * 5 * 5 * 17 * 29 * 37 * 149.

a(2) = 10460353204 = (2^0)*(3^21)+1 = 2 * 2 * 7 * 7 * 43 * 547 * 2269.

a(3) = 83682825625 = (2^3)*(3^21)+1 = 5 * 5 * 5 * 5 * 7 * 631 * 30313.

a(4) = 669462604993 = (2^6)*(3^21)+1 = 7 * 13 * 19 * 31 * 67 * 277 * 673.

a(7) = 7625597484988 = (2^0)*(3^27)+1 = 2 * 2 * 7 * 19 * 37 * 19441 * 19927.

a(9) = 35184372088833 = (2^45)*(3^0)+1 = 3 * 3 * 3 * 11 * 19 * 331 * 18837001.

a(13) = 1125899906842625 = (2^50)*(3^0)+1 = 5 * 5 * 5 * 41 * 101 * 8101 * 268501.

a(16) = 5559060566555524 = (2^0)*(3^33)+1 = 2 * 2 * 7 * 67 * 661 * 25411 * 176419.

a(28) = 9223372036854775809 = (2^63)*(3^0)+1 = 3 * 3 * 3 * 19 * 43 * 5419 * 77158673929.

PROG

(PARI) list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==7, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

CROSSREFS

Intersection of A046308 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.

A111346 gives the Pierpont 6-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: A233703 A230085 A204337 * A159448 A316745 A015381

Adjacent sequences:  A113736 A113737 A113738 * A113740 A113741 A113742

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Nov 08 2005

EXTENSIONS

Extended by Ray Chandler, Nov 08 2005

STATUS

approved

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Last modified October 20 10:43 EDT 2021. Contains 348100 sequences. (Running on oeis4.)