A160357 Sign of first differences of Recamán's sequence A005132.

1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1

Offset: 0

Author

M. F. Hasler, Jun 03 2009

Keywords

• sign

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005132, A119632.

Programs

Maple

A160357 := proc(n)
        sign( A005132(n)-A005132(n-1)) ;
end proc: # R. J. Mathar, Apr 01 2012

Mathematica

f[s_List] := Module[{a = s[[-1]], n = Length[s]}, Append[s, If[a > n && FreeQ[s, a - n], a - n, a + n]]];
Nest[f, {0}, 100] // Differences // Sign (* Jean-François Alcover, Apr 19 2020, using Robert G. Wilson v's code for A005132 *)

Formula

a(n) = sign(A005132(n)-A005132(n-1)) = sign(A160356(n)) = (-1)^A160351(n) = -(-1)^A076213(n-1).

a(n) = (A005132(n)-A005132(n-1))/n. - N. J. A. Sloane, Jul 15 2011

A160357 = chi_A057165 - chi_A057166, where chi_A denotes the characteristic function of (the set of values of) A.

Extensions

a(0)=1 added by N. J. A. Sloane, May 01 2020