A057167 Term in Recamán's sequence A005132 where n appears for first time, or -1 if n never appears.

0, 1, 4, 2, 131, 129, 3, 5, 16, 14, 12, 10, 8, 6, 31, 29, 27, 25, 23, 99734, 7, 9, 11, 13, 15, 17, 64, 62, 60, 58, 56, 54, 52, 50, 48, 46, 44, 42, 40, 38, 111, 22, 20, 18, 28, 30, 32, 222, 220, 218, 216, 214, 212, 210, 208, 206, 204, 202, 200, 198, 196

Offset: 0

Author

N. J. A. Sloane, Sep 14 2000

Keywords

• nonn
• easy
• nice
• look

Links

• T. D. Noe, Table of n, a(n) for n=0..1642 (taking a(1355) from A064227)
• Nick Hobson, Python program for this sequence
• C. L. Mallows, Plot (jpeg) of first 10000 terms of A005132
• C. L. Mallows, Plot (postscript) of first 10000 terms of A005132
• N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
• N. J. A. Sloane, FORTRAN program for A005132, A057167, A064227, A064228
• Index entries for sequences related to Recamán's sequence

Crossrefs

Cf. A005132, A057165, A057166.

Cf. also A187943, A187922.

Programs

Maple

w := array(1..10000); for j from 1 to 100 do l := 0; for k from 1 to nops(a) do if a[k] = j then l := k; exit; fi; od: w[j] := l; od: s := [seq(w[j],j=1..100)]; # where a is an array formed from sequence A005132

Mathematica

A005132 = {0}; Do[If[(r = Last[A005132] - n) <= 0 || MemberQ[ A005132, r], r = r + 2n]; AppendTo[ A005132, r], {n, 1, 10^5}]; a[n_] := If[p = Position[ A005132, n]; p == {}, 0, p[[1, 1]] - 1]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jul 18 2012 *)

PARI

first(n) = my(a=vector(n), r=[0]); while(#Set(a)Iain Fox, Jul 11 2022

Python

from itertools import count, islice
def agen(): # generator of terms
    an, A005132set, inv, y = 0, {0}, {0: 0}, 0
    for n in count(1):
        t = an - n
        an = t if t >= 0 and t not in A005132set else an + n
        A005132set.add(an)
        inv[an] = n
        while y in inv: yield inv[y]; y += 1
print(list(islice(agen(), 61))) # Michael S. Branicky, Jul 12 2022

Extensions

I conjecture a(n) is never -1 - but see A064227, A064228.

a(0)=0 added and escape clause value changed to -1 by N. J. A. Sloane, May 01 2020