

A240753


Number of values of k such that n + k + 1 and n + n/k + 1 are both prime.


1



1, 0, 2, 1, 2, 0, 0, 2, 3, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 4, 1, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 3, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2
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OFFSET

1,3


COMMENTS

a(n) is not 0 for n = 1, 3, 4, 5, 8, 9, 11, 15, 20, 21, 24, 25, 27, 28, 29, ...  Michel Marcus, Apr 16 2014


LINKS

Table of n, a(n) for n=1..95.


EXAMPLE

a(9) = 3 because
1) 9 + 1 + 1 = 11 and 9 + 9/1 + 1 = 19 are both prime for value of k = 1,
2) 9 + 3 + 1 = 13 and 9 + 9/3 + 1 = 13 are both prime for value of k = 3,
3) 9 + 9 + 1 = 19 and 9 + 9/9 + 1 = 11 are both prime for value of k = 9.


MAPLE

with(numtheory): A240753 := proc (n) local ct, k: ct := 0: for k in divisors(n) do if isprime(n+k+1) and isprime(n+n/k+1) then ct := ct+1: end if end do: return ct: end proc: seq(A240753(n), n = 1 .. 100); # Nathaniel Johnston, Apr 15 2014


PROG

(PARI) for(n=1, 100, m=0; fordiv(n, k, if(isprime(n+k+1) && isprime(n+n/k+1), m++)); print1(m, ", ")) \\ Colin Barker, Apr 12 2014


CROSSREFS

Sequence in context: A287411 A053796 A029391 * A202149 A236533 A298187
Adjacent sequences: A240750 A240751 A240752 * A240754 A240755 A240756


KEYWORD

nonn


AUTHOR

Ilya Lopatin and JuriStepan Gerasimov, Apr 12 2014


EXTENSIONS

Several terms and the example corrected by Colin Barker, Apr 13 2014


STATUS

approved



