A226859 Number of prime sums in the process described in A226770.

1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 3, 1, 3, 2, 3, 1, 4, 1, 4, 2, 5, 1, 5, 1, 6, 3, 7, 1, 6, 1, 7, 4, 7, 3, 8, 1, 9, 4, 9, 1, 9, 1, 9, 4, 10, 1, 9, 2, 10, 2, 11, 1, 11, 2, 13, 5, 14, 1, 13, 1, 12, 5, 12, 5, 13, 1, 13, 6, 14, 1, 14, 1, 13, 6, 14, 7, 15, 1, 15, 3, 15

Offset: 1

Author

Vladimir Shevelev, Jun 20 2013

Keywords

• nonn

Examples

			Let n=76. We have 77; d=7,11; 76+7=83 (prime), 76+11=87; d=3,29; 76+3=79(prime), 76+29=105; d=5,15,21,35; 76+5=81, 76+15=91, 76+21=97(prime), 76+35=111; d=9,27,13,37, 76+9=85,76+27=103(prime),76+13=89(prime), 76+37=113(prime), d=17, 76+17=93; d=31, 76+31=107(prime). Thus the set of prime sums is {83,79,97,103,89,113,107} and therefore a(76)=7.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A226770, A226856, A053184.

Programs

Mathematica

Table[(div=Most[Divisors[n+1]]; Count[n+FixedPoint[Union[Flatten[AppendTo[div, Map[Most[Divisors[n+#]]&, #]]]]&, div],?PrimeQ]),{n,50}] (* _Peter J. C. Moses, Jun 20 2013 *)

Formula

a(n) = 1 iff either n = 5 or n + 1 = p or n + 1 = q^2, where p,q and q^2+q-1 are primes.

Extensions

More terms from Peter J. C. Moses, Jun 20 2013