A187943 -id:A187943 - cp's OEIS frontend

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

N. J. A. Sloane, Sep 14 2000

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

Cf. A005132, A057165, A057166.

Cf. also A187943, A187922.

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

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 *)

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

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

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

A187922 Positions k of addition steps in Recamán's sequence where A005132(k-1)-k = A005132(m) for some 0 < m < k.

Original entry on oeis.org

6, 7, 9, 18, 19, 21, 33, 34, 36, 66, 67, 69, 71, 73, 75, 101, 102, 104, 106, 108, 113, 114, 115, 117, 121, 123, 125, 127, 133, 134, 172, 173, 175, 177, 179, 181, 183, 186, 188, 189, 190, 194, 224, 225, 227, 229, 231, 233, 236, 238, 240, 242, 244, 246, 287, 288, 290, 292, 294, 296, 298, 300, 302, 304, 339, 340, 342, 344, 346, 348, 350

Offset: 1

Reinhard Zumkeller, Mar 17 2011

nonn

Subsequence of A057165; A005132(a(n)-1) - a(n) = A005132(A187943(n));
A005132(a(n)) = A005132(a(n)-1) + a(n);
See A187921 for the other positions of addition steps in A005132.

			a(5) = 19: A005132(19-1) = 43 and 43-19>0, but the term 24=43-19 is already in A005132, therefore A005132(19)=43+19=62; A187943(5)=15 and A005132(15)=24.

Rémy Sigrist, Table of n, a(n) for n = 1..25000
Rémy Sigrist, C++ program for A187943
Index entries for sequences related to Recamán's sequence

Cf. A005132, A057165, A187921, A187943, A333548, A333552.

import Data.Set (Set, singleton, member, insert)
a187922 n = a187922_list !! (n-1)
a187922_list = r (singleton 0) 1 0 where
   r :: Set Integer -> Integer -> Integer -> [Integer]
   r s n x | x <= n           = r (insert (x+n) s) (n+1) (x+n)
           | (x-n) `member` s = n : r (insert (x+n) s) (n+1) (x+n)
           | otherwise        = r (insert (x-n) s) (n+1) (x-n)
(C++) See Links section.

Added condition "0 < m" to definition. See A333552. - N. J. A. Sloane, May 04 2020

cp's OEIS Frontend

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

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