

A295741


a(n) is smallest divisor d of the nth primorial such that d + prime(n)#/d is prime.


1



1, 1, 1, 1, 1, 1, 2, 5, 6, 10, 2, 1, 2, 11, 7, 2, 41, 2, 5, 5, 5, 3, 51, 10, 3, 14, 37, 10, 7, 2, 17, 17, 62, 21, 3, 38, 17, 47, 13, 17, 13, 7, 21, 83, 10, 138, 10, 26, 2, 7, 19, 31, 15, 13, 5, 23, 103, 19, 5, 95, 61, 6, 15, 2, 35, 13, 19, 65, 39, 7, 43, 73, 13, 26, 97, 1, 91, 2, 78, 19, 39, 34, 167, 82, 10, 38, 66, 58, 2, 46, 71
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OFFSET

0,7


COMMENTS

Conjecture: a(n) < prime(n)^2 for n > 0.
a(n) = 1 iff n belongs to A014545.
Inspired by A293756.


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 0..1000


EXAMPLE

a(3) = 1 because 1 + prime(3)#/1 = 1 + 2*3*5 = 31 and 31 is a prime;
a(6) = 2 because 2 + prime(6)#/2 = 2 + 2*3*5*7*11*13/2 = 15017 and that is a prime;
a(7) = 5 because 5 + prime(7)#/5 = 5 + 2*3*5*7*11*13*17/5 = 102107 which is a prime; etc.


MATHEMATICA

f[n_] := Block[{d = 1, p = Fold[Times, 1, Prime@ Range@ n]}, While[ !PrimeQ[d + p/d], d++]; d]; Array[f, 90]


PROG

(PARI) a(n)=my(P=vecprod(primes(n))); for(d=1, P, if(P%d==0 && ispseudoprime(d+P/d), return(d))) \\ Charles R Greathouse IV, Nov 27 2017


CROSSREFS

Cf. A002110, A005235, A014545.
Sequence in context: A122965 A226810 A054463 * A007503 A184418 A112967
Adjacent sequences: A295738 A295739 A295740 * A295742 A295743 A295744


KEYWORD

nonn


AUTHOR

Thomas Ordowski and Robert G. Wilson v, Nov 26 2017


STATUS

approved



