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

Author

Reinhard Zumkeller, Oct 15 2008

Keywords

• nonn

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

Crossrefs

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

See also A010051, A192490.

Programs

Mathematica

luckies = 2 Range[0, 100] + 1;
Module[{k, r}, For[k = 2, k 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 *)

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

Formula

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