A240753 Number of values of k such that n + k + 1 and n + n/k + 1 are both prime.

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

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: A053796 A029391 A058087 * A202149 A236533 A298187

Adjacent sequences: A240750 A240751 A240752 * A240754 A240755 A240756

Keyword

nonn

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Apr 12 2014

Extensions

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

Status

approved