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

2,1

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.

Links

Table of n, a(n) for n=2..22.

Index entries for sequences related to lucky numbers

Formula

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

Example

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).

Crossrefs

First column of A350003.

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

Sequence in context: A336480 A075400 A222293 * A242556 A087366 A324249

Adjacent sequences: A349999 A350000 A350001 * A350003 A350004 A350005

Keyword

nonn,more

Author

Pontus von Brömssen, Dec 08 2021

Status

approved