A250293 -id:A250293 - cp's OEIS frontend

A085725 Numbers k such that 1 + (product of first k primes) is a semiprime.

6, 8, 9, 14, 18, 19, 21, 23, 26, 34, 36, 40, 48, 54, 76, 88, 105, 122, 135

Offset: 1

Jason Earls, Jul 20 2003

See A250293 for more information.

Cf. A001358 (semiprimes), A002110, A006862 (Euclid numbers), A250293.

isok(k) = bigomega(1 + prod(j=1, k, prime(j))) == 2; \\ Michel Marcus, Mar 30 2019

a(n) = primepi(A250293(n)). - Hugo Pfoertner, Feb 05 2021

More terms from David Wasserman, Feb 09 2005
a(14)=54 from Donovan Johnson, Feb 21 2008
Offset changed to 1 by Alois P. Heinz, Jul 02 2015
a(15) added by Daniel Suteu, Mar 30 2019
a(16)-a(18) using terms of A250293 from Hugo Pfoertner, Feb 05 2021
Missing 105 inserted by Sean A. Irvine, Mar 03 2023

A250294 Primes p such that p#-1 is a semiprime, where # is the primorial (A034386).

Original entry on oeis.org

7, 17, 29, 31, 43, 59, 71, 73, 97, 101, 223, 233, 257, 439, 503, 709, 859, 863, 1013

Offset: 1

Eric Chen, Dec 24 2014

1153 and 1381 are also terms. - Amiram Eldar, Feb 16 2020

a(20) >= 1091. 1091# - 1 is a 458-digit composite with no known factors. - Hugo Pfoertner, Feb 05 2021

			a(2) = 17 so 17# - 1 = 510509 = 61 * 8369 is a semiprime.

FactorDB Factorization of 1013#-1.
FactorDB Status of 1091#-1.
Hisanori Mishima, Factorizations of many number sequences, PI Pn - 1 (n = 1 to 110) (2013).

Cf. A001221, A001358, A002110, A006794, A034386, A057588, A078781, A250293.

p = Select[Range[101], PrimeQ]; p[[ Position[FoldList[Times, p] - 1, ?(PrimeOmega[#] == 2 &)] //Flatten ]] (* _Amiram Eldar, Feb 16 2020 *)

A001221(A034386(a(n)) - 1) = 2. - Amiram Eldar, Feb 16 2020

a(15)-a(18) using factordb.com from Amiram Eldar, Feb 16 2020
a(19) using factordb.com from Hugo Pfoertner, Feb 05 2021
Edited by Max Alekseyev, Aug 26 2021

cp's OEIS Frontend

A085725 Numbers k such that 1 + (product of first k primes) is a semiprime.

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