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A112797 Pierpont 3-almost primes. 3-almost primes of form (2^K)*(3^L)+1. 6
28, 244, 325, 385, 730, 1025, 1729, 2188, 5185, 6562, 7777, 16385, 26245, 36865, 46657, 49153, 55297, 82945, 93313, 221185, 354295, 419905, 531442, 559873, 589825, 663553, 708589, 884737, 1119745, 1572865, 1594324, 1889569, 2985985 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..33.

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) = 3.

EXAMPLE

a(1) = 28 = (2^0)*(3^3)+1 = 2 * 2 * 7.

a(2) = 244 = (2^0)*(3^5)+1 = 2 * 2 * 61.

a(3) = 325 = (2^2)*(3^4)+1 = 5 * 5 * 13.

a(4) = 385 = (2^7)*(3^1)+1 = 5 * 7 * 11.

a(11) = 7777 = (2^5)*(3^5)+1 = 7 * 11 * 101.

a(115) = 94143178828 = (2^0)*(3^23)+1 = 2 * 2 * 23535794707.

a(119) = 137438953473 = (2^37)*(3^0)+1 = 3 * 1777 * 25781083.

a(196) = 281474976710657 = (2^48)*(3^0)+1 = 193 * 65537 * 22253377.

MATHEMATICA

Take[Select[2^#[[1]] 3^#[[2]] + 1 & /@ Tuples[Range[0, 20], 2],

PrimeOmega[ #]  ==  3 &] // Union, 40] (* Harvey P. Dale, Jan 02 2021 *)

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)==3, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

CROSSREFS

Intersection of A014612 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.

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.

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: A223347 A242436 A119544 * A085438 A188526 A219600

Adjacent sequences:  A112794 A112795 A112796 * A112798 A112799 A112800

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 08 2005

EXTENSIONS

Extended by Ray Chandler, Nov 08 2005

STATUS

approved

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Last modified June 19 20:27 EDT 2021. Contains 345145 sequences. (Running on oeis4.)