

A261628


Least prime p such that n(p*n'1) and n+(p*n'1) are both prime where n' = (3+(1)^n)/2, or 0 if no such prime p exists.


2



0, 0, 0, 0, 3, 0, 5, 2, 3, 2, 7, 3, 7, 2, 3, 2, 7, 3, 13, 2, 3, 5, 7, 3, 7, 2, 5, 5, 13, 7, 13, 5, 5, 2, 7, 3, 7, 5, 3, 2, 13, 3, 31, 2, 3, 17, 7, 3, 13, 2, 11, 5, 7, 7, 13, 2, 5, 11, 13, 7, 19, 5, 5, 2, 7, 3, 7, 11, 3, 2, 13, 13, 7, 17, 5, 2, 7, 3, 19, 5
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OFFSET

1,5


COMMENTS

Conjecture: 0 < a(n) < sqrt(2*n)*log(5*n) for all n > 6.
See also A261627.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei Sun, Conjectures involving primes and quadratic forms, arXiv:1211.1588 [math.NT], 20122015.


EXAMPLE

a(43) = 31 since 31, 43(311) = 13 and 43+(311) = 73 are all prime.
a(72) = 13 since 13, 72(2*131) = 47 and 72+(2*131) = 97 are all prime.


MATHEMATICA

Do[Do[If[PrimeQ[n(3+(1)^n)/2*Prime[k]+1]&&PrimeQ[n+(3+(1)^n)/2*Prime[k]1], Print[n, " ", Prime[k]]; Goto[aa]], {k, 1, PrimePi[2n/(3+(1)^n)]}]; Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 80}]


CROSSREFS

Cf. A000040, A002372, A002375, A046927, A261627.
Sequence in context: A130054 A236146 A196111 * A007431 A215447 A159980
Adjacent sequences: A261625 A261626 A261627 * A261629 A261630 A261631


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Aug 27 2015


STATUS

approved



