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

1999004627104432129, 4052555153018976268, 8754997675608244225, 9606056659007943745, 11832592569282330625, 22769912080611422209, 68309736241834266625, 354577405862133891073, 12449449430074295092225

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..993

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) = 8.

Example

a(1) = 1999004627104432129 = (2^18)*(3^27)+1 = 7 * 13 * 19 * 109 * 127 * 181 * 6949 * 66403.
a(2) = 4052555153018976268 = (2^0)*(3^39)+1 = 2 * 2 * 7 * 79 * 157 * 2887 * 10141 * 398581.
a(3) = 8754997675608244225 = (2^55)*(3^5)+1 = 5 * 5 * 11 * 11 * 1201 * 1229 * 16451 * 119191.
a(4) = 9606056659007943745 = (2^6)*(3^36)+1 = 5 * 13 * 17 * 89 * 109 * 281 * 18793 * 169693.
a(13) = 717897987691852588770250 = (2^0)*(3^50)+1 = 2 * 5 * 5 * 5 * 101 * 1181 * 394201 * 61070817601.
a(29) = 1570042899082081611640534564 = (2^0)*(3^57)+1 = 2 * 2 * 7 * 2851 * 3079 * 53923 * 101917 * 1162320517.

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)==8, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 06 2017

Crossrefs

Intersection of A046310 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.

A113739 gives the Pierpont 7-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: A113741 A115529 A229864 * A281508 A281509 A115539

Adjacent sequences: A113737 A113738 A113739 * A113741 A113742 A113743

Keyword

nonn

Author

Jonathan Vos Post, Nov 08 2005

Extensions

Extended by Ray Chandler, Nov 08 2005

Status

approved