A256119 Least number p that is zero or an odd prime, such that n - p is a generalized pentagonal number.

0, 0, 0, 3, 3, 0, 5, 0, 3, 7, 3, 11, 0, 11, 7, 0, 11, 5, 3, 7, 5, 19, 0, 11, 17, 3, 0, 5, 13, 3, 23, 5, 17, 7, 19, 0, 29, 11, 3, 13, 0, 19, 7, 3, 29, 5, 11, 7, 13, 23, 43, 0, 17, 13, 3, 29, 5, 0, 7, 19, 3, 59, 5, 23, 7, 43, 31, 41, 11, 29, 0, 31, 37, 3, 17, 5, 19, 0, 43, 53, 3, 11, 5, 13, 7, 59, 29, 17, 11, 19, 13, 79, 0, 23, 17, 3, 19, 5, 41, 7, 0

Offset

0,4

Comments

By the conjecture in A256071, a(n) always exists.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 0..10000

Example

a(21) = 19 since 21 is not a generalized pentagonal number, and 19 is the least odd prime p with 21 - p a generalized pentagonal number.
a(26) = 0 since 26 = (-4)*(3*(-4)-1)/2 is a generalized pentagonal number.

Mathematica

Pen[n_]:=IntegerQ[Sqrt[24n+1]]
Do[If[Pen[n], Print[n, " ", 0]; Goto[aa]]; Do[If[Pen[n-Prime[k]], Print[n, " ", Prime[k]]; Goto[aa]], {k, 2, PrimePi[n]}]; Label[aa]; Continue, {n, 0, 100}]

Crossrefs

Cf. A000040, A001318, A256071.

Sequence in context: A116580 A096439 A377143 * A217552 A128046 A102899

Adjacent sequences: A256116 A256117 A256118 * A256120 A256121 A256122

Keyword

nonn

Author

Zhi-Wei Sun, Mar 15 2015

Status

approved