A350002 a(n) is the smallest lucky number L(k) such that the n-th difference of (L(k), ..., L(k+n)) is zero, where L is A000959; a(n) = 0 if no such number exists.

37, 31, 87, 31, 517, 1797, 1797, 267, 483, 5649, 23815, 198223, 985921, 508401, 3720765, 1936245, 8302279, 16713091, 9857049, 16756749, 8904175

Offset: 2

Author

Pontus von Brömssen, Dec 08 2021

Keywords

• nonn
• more

Comments

Equivalently, a(n) is the smallest lucky 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) = A000959(k), where k is the smallest positive integer such that A350001(n,k) = 0.

Examples

			The first six consecutive lucky numbers for which the fifth difference is 0 are (31, 33, 37, 43, 49, 51), so a(5) = 31. The successive differences are (2, 4, 6, 6, 2), (2, 2, 0, -4), (0, -2, -4), (-2, -2), and (0).
		

Links

• Index entries for sequences related to lucky numbers

Crossrefs

First column of A350003.

Cf. A000959, A349643 (counterpart for primes), A350001, A350006 (counterpart for ludic numbers).

Formula

Sum_{j=0..n} (-1)^j*binomial(n,j)*A000959(k+j) = 0, where A000959(k) = a(n).