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

1,7

Links

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

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.

Example

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.

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 *)

Crossrefs

Cf. A226770, A226856, A053184.

Sequence in context: A029236 A152188 A239930 * A025820 A109704 A073407

Adjacent sequences: A226856 A226857 A226858 * A226860 A226861 A226862

Keyword

nonn

Author

Vladimir Shevelev, Jun 20 2013

Extensions

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

Status

approved