A145649 Characteristic function of the lucky numbers.

1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1

Offset

1,1

Comments

Is there an efficient formula for this sequence? To wit, is there an algorithm for determining whether n is a lucky or unlucky number which is substantially faster than determining the lucky numbers up to n? - Charles R Greathouse IV, Nov 24 2021

Links

Antti Karttunen, Table of n, a(n) for n = 1..100005

Eric Weisstein's World of Mathematics, Lucky Numbers

Index entries for characteristic functions

Index entries for sequences generated by sieves

Formula

a(A000959(n)) = 1, a(A050505(n)) = 0.

Mathematica

luckies = 2 Range[0, 100] + 1;
Module[{k, r}, For[k = 2, k<Length[luckies], r = luckies[[k++]]; luckies = ReplacePart[luckies, Table[r*i -> Nothing, {i, 1, Length[luckies]/r}]]]];
a[n_ /; 1 <= n <= Last[luckies]] := Boole[MemberQ[luckies, n]];
Table[a[n], {n, 1, Last[luckies]}] (* Jean-François Alcover, Oct 18 2021, after Robert Israel in A000959 *)

Prog

(PARI) A145649list(up_to) = { my(u=A000959_upto(up_to), v=vector(up_to)); for(i=1, #u, v[u[i]] = 1); (v); }; \\ See there for A000959_upto(). - Antti Karttunen, Sep 27 2019

Crossrefs

Cf. A000959 (lucky numbers), A050505 (complement: unlucky numbers).

See also A010051, A192490.

Sequence in context: A015605 A015437 A015101 * A016340 A014021 A015725

Adjacent sequences: A145646 A145647 A145648 * A145650 A145651 A145652

Keyword

nonn

Author

Reinhard Zumkeller, Oct 15 2008

Status

approved