A076213 -id:A076213 - cp's OEIS frontend

A076258 a(n) = 2 * Sum_{k=1..n} A076213(k) - n.

1, 2, 1, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 5, 6, 5, 6, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 9, 8, 9, 8, 9

Offset: 1

Benoit Cloitre, Nov 05 2002

nonn

Cf. A005132.

It seems that a(n)>0, a(n)/log(n) is bounded and sum(k=1, n, a(k)) is asymptotic to c*n*log(n) 1 < c < 1.5.

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

Original entry on oeis.org

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

M. F. Hasler, Jun 03 2009

sign

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

Cf. A005132, A119632.

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

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 *)

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.

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

A160351 Characteristic function of A057166.

Original entry on oeis.org

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

Offset: 1

M. F. Hasler, Jun 03 2009

nonn

Index entries for sequences related to Recamán's sequence

a(n) = (1-A160357(n))/2 = 1-A076213(n-1).

cp's OEIS Frontend

A076258 a(n) = 2 * Sum_{k=1..n} A076213(k) - n.

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

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A160351 Characteristic function of A057166.

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