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

1,9

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).

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A000196, A010051.

Sequence in context: A035169 A340728 A275851 * A364011 A192174 A262202

Adjacent sequences: A067429 A067430 A067431 * A067433 A067434 A067435

Keyword

nonn

Author

Reinhard Zumkeller, Feb 15 2002

Status

approved