A079644 n (mod sqrtint(n)).

0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 3, 0, 1, 2, 3, 0, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 1, 2, 3, 4, 5

Offset

1,11

Comments

Record values: given an m>=0, the first n for which a(n)=m is n = (m+1)^2+m = A028387(m). Also, for n>3, n is a square if and only if a(n)=0 and a(n-1)=0. - Stanislav Sykora, Aug 13 2014

Links

Stanislav Sykora, Table of n, a(n) for n = 1..1023

Formula

a(A006446(n))=0; a(A033638(n))=1.

When n>0, a(A000290(n))=0; when n>1, a(A000290(n)-1)=0. - Stanislav Sykora, Aug 13 2014

a(n) = 0 if n or n+1 or 4*n+1 is a square, otherwise a(n) = a(n-1)+1. - Robert Israel, Aug 13 2014

G.f.: sum(r=2..infinity, x^(r^2) * (x^r + 1) * ((r-1)*x^(r+1) - r*x^r + x)/(1 - x)^2. - Robert Israel, Aug 13 2014

Maple

a:= proc(n) local r;
r:= isqrt(n);
if r^2 > n then r:= r-1 fi;
n mod r;
end proc:
seq(a(n), n=1..100); # Robert Israel, Aug 13 2014

Mathematica

A079644[n_]:=Mod[n, Floor[n^(1/2)]]; Array[A079644, 200] (* Enrique Pérez Herrero, Oct 06 2011 *)
Table[Mod[n, Floor[Sqrt[n]]], {n, 110}] (* Harvey P. Dale, Apr 10 2016 *)

Prog

(PARI) a(n)=n%sqrtint(n)

Crossrefs

Cf. A000290, A006446, A028387, A033638.

Sequence in context: A322823 A334872 A263844 * A072705 A072574 A293595

Adjacent sequences: A079641 A079642 A079643 * A079645 A079646 A079647

Keyword

nonn

Author

Benoit Cloitre, Jan 31 2003

Status

approved