A057167 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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

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 *)

PROG

(PARI) first(n) = my(a=vector(n), r=[0]); while(#Set(a)<n, my(i=#r, j=r[i]-i, k=j+(j<1 || setsearch(Set(r), j))*2*i); r=concat(r, [k]); if(k<n && !a[k+1], a[k+1]=i)); 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

CROSSREFS