

A078783


a(0) = 0; a(1)=1; for n>1, a(n) = least positive integer m not among a(1),...,a(n1) such that ma(n1) > a(n1)a(n2).


8



0, 1, 3, 6, 2, 7, 13, 4, 14, 25, 5, 26, 48, 8, 49, 91, 9, 92, 176, 10, 177, 345, 11, 346, 682, 12, 683, 1355, 15, 1356, 2698, 16, 2699, 5383, 17, 5384, 10752, 18, 10753, 21489, 19, 21490, 42962, 20, 42963, 85907, 21, 85908, 171796, 22, 171797
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OFFSET

0,3


COMMENTS

This is a permutation pi of the nonnegative integers such that pi(n+1)pi(n) is strictly increasing. In other words, it is a walk on the nonnegative numbers with strictly increasing step size which visits every number exactly once.
A greedy version of Recamán's sequence: Construct two sequences a() and d() as follows. a(0)=0, a(1)=1, a(2)=3, d(0)=0, d(1)=1, d(2)=2. For n>=3, let m be smallest nonnegative number not yet in the a sequence. Let i = a(n1)m. If i > d(n), then a(n) = a(n1)i = m, d(n) = i; otherwise a(n) = a(n1)+d(n1)+1, d(n) = d(n1)+1. Has the properties that a() is the Recamán transform of d() and every number appears in a(). This sequence is a(), while d() is A117073. Has a natural decompostion into segments of length 3.  N. J. A. Sloane, Apr 16 2006
For n>0: a(3*n2)=A117070(n), a(3*n1)=A117071(n) and a(3*n)=A117072(n).


REFERENCES

N. J. A. Sloane and Allan Wilks, On sequences of Recaman type, paper in preparation, 2006.


LINKS

Paul Tek, Table of n, a(n) for n = 0..2000
Index entries for sequences that are permutations of the natural numbers


MATHEMATICA

a[0] = 0; a[1] = 1;
a[n_] := a[n] = For[m = 2, True, m++, If[FreeQ[Array[a, n1], m], If[Abs[m  a[n1]] > Abs[a[n1]  a[n2]], Return[m]]]];
Table[a[n], {n, 0, 50}] (* JeanFrançois Alcover, Aug 02 2018 *)


PROG

(Haskell)
import Data.List (delete)
a078783 n = a078783_list !! n
(a078783_list, a117073_list) = unzip $
(0, 0) : (1, 1) : (3, 2) : f 3 2 (2:[4..]) where
f a d ms@(m:_) = (a', d') : f a' d' (delete a' ms) where
(a', d') = if i > d then (m, i) else (a + d + 1, d + 1)
i = a  m
 Reinhard Zumkeller, May 01 2015


CROSSREFS

Cf. A072007, A005132, A117070A117075.
Cf. A257502 (inverse).
Sequence in context: A169750 A249558 A072007 * A273465 A328503 A125717
Adjacent sequences: A078780 A078781 A078782 * A078784 A078785 A078786


KEYWORD

easy,nonn


AUTHOR

Reiner Martin (reinermartin(AT)hotmail.com), Jan 09 2003


STATUS

approved



