A350006 a(n) is the smallest ludic number L(k) such that the n-th difference of (L(k), ..., L(k+n)) is zero, where L is A003309; a(n) = 0 if no such number exists.

1, 11, 41, 47, 91, 1361, 4261, 481, 46067, 5027, 31499, 888893, 126205, 36191, 7676353, 26794127, 206527, 2560375, 7716073

Offset: 2

Author

Pontus von Brömssen, Dec 08 2021

Keywords

• nonn
• more

Comments

Equivalently, a(n) is the smallest ludic number L(k) such that there is a polynomial f of degree at most n-1 such that f(j) = L(j) for k <= j <= k+n.

a(n) = A003309(k), where k is the smallest positive integer such that A350004(n,k) = 0.

a(21) > 10^8 (unless a(21) = 0).

Examples

			The first six consecutive ludic numbers for which the fifth difference is 0 are (47, 53, 61, 67, 71, 77), so a(5) = 47. The successive differences are (6, 8, 6, 4, 6), (2, -2, -2, 2), (-4, 0, 4), (4, 4), and (0).
		

Crossrefs

First column of A350007.

Cf. A003309, A349643, A350002, A350004.

Formula

Sum_{j=0..n} (-1)^j*binomial(n,j)*A003309(k+j) = 0, where A003309(k) = a(n).