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A190617 The smallest prime q <= prime(n) such that 1 + q# * prime(n)# is prime, or 0 if no such q exists. 1
2, 2, 2, 2, 2, 3, 0, 19, 13, 13, 2, 11, 0, 3, 0, 7, 3, 2, 0, 0, 3, 0, 2, 0, 7, 2, 0, 0, 7, 2, 0, 0, 5, 13, 17, 5, 0, 29, 73, 53, 0, 41, 17, 0, 61, 113, 67, 0, 23, 7, 31, 53, 3, 0, 0, 109, 13, 43, 101, 67, 113, 0, 181, 37, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The notation # refers to the primorials A002110, the partial products of primes.

Roughly 75% of the entries are nonzero.

For roughly 50% of the solutions (that is roughly 1/3 of all entries if zeros are included) the q are smaller than prime(n)/5.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..750

EXAMPLE

2*2 + 1 = 5 (prime) with q=2, q#=2, prime(n)# = 2 so a(1)=2.

2*2*3 + 1 = 13 (prime) with q=2, q#=2, prime(2)# = 2*3 so a(2)=2.

2*2*3*5 + 1 = 61 (prime) with q=2, q#=2, prime(3)# = 2*3*5 so a(3)=2.

2*2*3*5*7 + 1 = 421 (prime) with q=2, q#=2, prime(4)# = 2*3*5*7 so a(4)=2.

MAPLE

A002110 := proc(n) option remember; mul(ithprime(i), i=1..n) ; end proc:

A190617 := proc(n) local psharp ; psharp := A002110(n) ; for i from 1 to n do if isprime(1+psharp*A002110(i)) then return ithprime(i) ; end if; end do: return 0 ; end proc:

seq(A190617(n), n=1..80) ; # R. J. Mathar, Jun 02 2011

PROG

PFGW from Primeformgroup for prime search and certification

pfgw64 -f in.txt , results in pfgw-prime.log and pfgw.log

in.txt scriptyfile

SCRIPT

DIM nn, 0

DIM kk

DIM mm

DIM jj

DIMS tt

LABEL loopn

SET nn, nn+1

IF nn>750 THEN END

SET kk, p(nn)

SET mm, 0

LABEL loopm

SET mm, mm+1

IF mm>nn THEN GOTO loopn

SET jj, p(mm)

SETS tt, %d, %d\,; kk; jj

PRP kk#*(jj#)+1, tt

IF ISPRIME THEN GOTO loopn

  IF ISPRP THEN GOTO loopn

goto loopm

CROSSREFS

Sequence in context: A139514 A330955 A330956 * A068323 A054990 A046921

Adjacent sequences:  A190614 A190615 A190616 * A190618 A190619 A190620

KEYWORD

nonn

AUTHOR

Pierre CAMI, May 14 2011

STATUS

approved

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Last modified February 23 16:16 EST 2020. Contains 332175 sequences. (Running on oeis4.)