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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.
2
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.
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
KEYWORD
nonn,more
AUTHOR
STATUS
approved