A067432 Number of ways to represent the n-th prime in form p*q+p+q, where p and q are primes (see A066938).

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

Offset: 1

Author

Reinhard Zumkeller, Feb 15 2002

Keywords

• nonn

Comments

a(A049084(A066938(n))) > 0; a(A049084(A198273(n))) = 0; a(A049084(A198277(n))) = n and a(A049084(m)) <> n for m < A198277(n). [Reinhard Zumkeller, Oct 23 2011]

a(n) < A072670(n).

Examples

			a(15) = 2 as A000040(15) = 47 = 3*11+3+11 = 5*7+5+7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000196, A010051.

Programs

Haskell

a067432 n = length [p | let prime_n = a000040 n,
   p <- takeWhile (< a000196 prime_n) a000040_list,
   let (q,m) = divMod (prime_n - p) (p + 1),
   m == 0, a010051 q == 1]
a067432_list = map a067432 [1..]
-- Reinhard Zumkeller, Oct 23 2011