A350006 - OEIS

%I #6 Dec 12 2021 20:29:33

%S 1,11,41,47,91,1361,4261,481,46067,5027,31499,888893,126205,36191,

%T 7676353,26794127,206527,2560375,7716073

%N 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.

%C 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.

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

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

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

%e 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).

%Y First column of A350007.

%Y Cf. A003309, A349643, A350002, A350004.

%K nonn,more

%O 2,2

%A _Pontus von Brömssen_, Dec 08 2021