A087429 a(n) = 1 if gpf(n) < gpf(n+1), otherwise 0, where gpf = A006530 (greatest prime factor).

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

Offset: 1

Author

Reinhard Zumkeller, Sep 02 2003

Keywords

• nonn

Comments

Equivalently, a(n) = 1 iff A061395(n+1) > A061395(n), otherwise a(n) = 0. - Giovanni Teofilatto, Jan 03 2008

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for characteristic functions

Crossrefs

Characteristic function of A070089.

Cf. A006530, A057427, A061395, A070087, A070221, A087430.

Programs

Mathematica

Join[{1}, Table[If[PrimePi[FactorInteger[n + 1][[ -1, 1]]] > PrimePi[FactorInteger[n][[ -1, 1]]], 1, 0], {n, 2, 90}]] (* Stefan Steinerberger, Jan 06 2008 *)
If[#[[1]]<#[[2]],1,0]&/@Partition[FactorInteger[#][[-1,1]]&/@Range[120],2,1] (* Harvey P. Dale, Nov 19 2023 *)

Formula

a(n) = A057427(1+A057427(A070221(n))).

a(p-1)=1 and a(p)=0 for primes p.

a(A070089(n)) = 1, a(A070087(n)) = 0, a(A087430(n)) = 0.

Extensions

Edited by N. J. A. Sloane, Jul 01 2008, at the suggestion of R. J. Mathar