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A250293 Primes p such that p#+1 is a semiprime, where # is the primorial (A034386). 2
13, 19, 23, 43, 61, 67, 73, 83, 101, 139, 151, 173, 223, 251, 383, 457, 673, 761 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The next candidate for a(19) is 859. 859# + 1 is a 359-digit composite with no known factors. - Hugo Pfoertner, Feb 05 2021

LINKS

Table of n, a(n) for n=1..18.

factordb.com, Status of 859#+1</>.

Hisanori Mishima, Factorizations of many number sequences, PI Pn + 1 (n = 1 to 110) (2012).

FORMULA

a(n) = prime(A085725(n)). - Hugo Pfoertner, Feb 05 2021

EXAMPLE

a(1) = 13 so 13# + 1 = 30031 = 59 * 509 is a semiprime.

MATHEMATICA

Prime[#]&/@(Module[{pmrl=FoldList[Times, Prime[Range[50]]]}, Position[ pmrl, _?(PrimeOmega[ #+1]==2&)]]//Flatten) (* Harvey P. Dale, Apr 29 2017 *)

CROSSREFS

Cf. A005234, A006862, A034386, A078778, A085725, A250294.

Sequence in context: A121877 A109902 A214031 * A058898 A227092 A123840

Adjacent sequences:  A250290 A250291 A250292 * A250294 A250295 A250296

KEYWORD

nonn,hard,more

AUTHOR

Eric Chen, Dec 24 2014

EXTENSIONS

a(16)-a(18) using factordb.com from Hugo Pfoertner, Feb 05 2021

STATUS

approved

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Last modified March 2 14:38 EST 2021. Contains 341751 sequences. (Running on oeis4.)