A235703 Number of ordered ways to write n = p + q with p a term of A234695 and q a term of A235592.

0, 0, 0, 1, 2, 2, 3, 3, 3, 3, 4, 2, 3, 2, 2, 4, 3, 3, 3, 3, 5, 5, 4, 3, 4, 4, 3, 5, 3, 1, 5, 5, 3, 5, 2, 4, 4, 3, 5, 4, 4, 4, 6, 5, 4, 6, 5, 3, 6, 6, 6, 5, 2, 3, 4, 3, 5, 5, 4, 5, 6, 4, 3, 6, 4, 3, 6, 4, 4, 5, 3, 5, 3, 5, 6, 6, 5, 3, 6, 4, 2, 4, 1, 4, 5, 4, 5, 7, 5, 4, 6, 9, 5, 6, 4, 2, 6, 6, 2, 6

Offset

1,5

Comments

Conjecture: a(n) > 0 for all n > 3, and a(n) = 1 only for n = 4, 30, 83.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

 a(4) = 1 since 4 = 2 + 2 with 2, prime(2) - 2 + 1 = 2 and 2*3 - prime(2) = 3 all prime.
a(30) = 1 since 30 = 3 + 27 with 3, prime(3) - 3 + 1 = 3 and 27*28 - prime(27) = 756 - 103 = 653 all prime.
a(83) = 1 since 83 = 13 + 70 with 13, prime(13) - 13 + 1 = 29 and 70*71 - prime(70) = 4970 - 349 = 4621 all prime.

Mathematica

p[n_]:=PrimeQ[Prime[n]-n+1]
q[n_]:=PrimeQ[n(n+1)-Prime[n]]
a[n_]:=Sum[If[p[Prime[k]]&&q[n-Prime[k]], 1, 0], {k, 1, PrimePi[n-1]}]
Table[a[n], {n, 1, 100}]

Crossrefs

Cf. A000040, A234695, A235330, A235508, A235592.

Sequence in context: A087182 A035453 A272605 * A366664 A097747 A285717

Adjacent sequences: A235700 A235701 A235702 * A235704 A235705 A235706

Keyword

nonn

Author

Zhi-Wei Sun, Jan 14 2014

Status

approved