A228430 Number of ways to write n = x + y (x, y > 0) with x^4 + y*(y+1)/2 prime.

0, 1, 1, 2, 2, 0, 2, 3, 2, 3, 2, 3, 4, 1, 2, 1, 4, 3, 1, 1, 6, 4, 2, 4, 4, 4, 1, 5, 3, 5, 6, 4, 6, 3, 5, 5, 6, 3, 3, 5, 5, 5, 9, 3, 3, 11, 6, 7, 4, 8, 7, 12, 7, 5, 10, 4, 3, 8, 8, 3, 11, 6, 5, 10, 4, 6, 14, 6, 3, 9, 3, 12, 12, 9, 3, 11, 6, 10, 15, 7, 7, 8, 3, 6, 11, 8, 11, 10, 7, 3, 11, 10, 7, 11, 4, 6, 13, 11, 9, 8

Offset

1,4

Comments

Conjecture: (i) a(n) > 0 except for n = 1, 6.

(ii) For any positive integer n not among 1, 3, 14, 25, there are positive integers x and y with x + y = n such that x^3 + y*(y+1)/2 is prime.

Links

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

Example

a(14) = 1 since 14 = 4 + 10 with 4^4 + 10*11/2 = 311 prime.
a(27) = 1 since 27 = 22 + 5 with 22^4 + 5*6/2 = 234271 prime.

Mathematica

a[n_]:=Sum[If[PrimeQ[x^4+(n-x)(n-x+1)/2], 1, 0], {x, 1, n-1}]
Table[a[n], {n, 1, 100}]

Crossrefs

Cf. A000040, A000217, A000583, A228425, A228428, A228429.

Sequence in context: A361869 A256750 A378213 * A241533 A370885 A072738

Adjacent sequences: A228427 A228428 A228429 * A228431 A228432 A228433

Keyword

nonn

Author

Zhi-Wei Sun, Nov 10 2013

Status

approved