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A111344 Pierpont 4-almost primes: numbers with exactly 4 prime divisors, not necessarily distinct, of the form 2^K*3^L + 1. 7
513, 13825, 32769, 59050, 110593, 157465, 177148, 186625, 262145, 279937, 497665, 1259713, 1327105, 2097153, 2125765, 2519425, 4718593, 4782970, 5668705, 6718465, 17915905, 18874369, 22674817, 33554433, 38263753, 56623105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..2500

Eric Weisstein's World of Mathematics, Pierpont Prime

Eric Weisstein's World of Mathematics, Almost Prime

EXAMPLE

a(1) = 513 = (2^9)*(3^0)+1 = 3 * 3 * 3 * 19.

a(2) = 13825 = (2^9)*(3^3)+1 = 5 * 5 * 7 * 79.

a(3) = 32769 = (2^15)*(3^0)+1 = 3 * 3 * 11 * 331.

a(4) = 59050 = (2^0)*(3^10)+1 = 2 * 5 * 5 * 1181.

a(10) = 279937 = (2^7)*(3^7)+1 = 7 * 7 * 29 * 197 (lots of sevens).

a(24) = 33554433 = (2^25)*(3^0) = 3 * 11 * 251 * 4051.

a(60) = 31381059610 = (2^0)*(3^22)+1 = 2 * 5 * 5501 * 570461.

a(168) = 16677181699666570 = (2^0)*(3^34)+1 = 2 * 5 * 956353 * 1743831169.

PROG

(PARI) is(n)=bigomega(n)==4 && n-1 == 2^valuation(n-1, 2)*3^valuation(n-1, 3) \\ Charles R Greathouse IV, Feb 01 2017

(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)==4, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

CROSSREFS

Intersection of A014613 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.

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: A066697 A076338 A237620 * A230188 A223651 A351272

Adjacent sequences:  A111341 A111342 A111343 * A111345 A111346 A111347

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Nov 08 2005

EXTENSIONS

Extended by Ray Chandler, Nov 08 2005

Name edited by Charles R Greathouse IV, Feb 01 2017

STATUS

approved

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Last modified May 17 08:05 EDT 2022. Contains 353741 sequences. (Running on oeis4.)