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A064389 Variation (4) on Recamán's sequence (A005132): to get a(n), we first try to subtract n from a(n-1): a(n) = a(n-1)-n if positive and not already in the sequence; if not then we try to add n: a(n) = a(n-1)+n if not already in the sequence; if this fails we try to subtract n+1 from a(n-1), or to add n+1 to a(n-1), or to subtract n+2, or to add n+2, etc., until one of these produces a positive number not already in the sequence - this is a(n). 9
1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 44, 19, 45, 72, 100, 71, 101, 70, 38, 5, 39, 4, 40, 77, 115, 76, 36, 78, 120, 163, 119, 74, 28, 75, 27, 79, 29, 80, 132, 185, 131, 186, 130, 73, 15, 81, 141, 202 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is the nicest of these variations. Is this a permutation of the natural numbers?

The number of steps before n appears is the inverse series, A078758. The height of n is in A126712.

See A078758 for the inverse permutation (in case this is a permutation of the positive integers). - M. F. Hasler, Nov 03 2014

After 10^12 terms, the smallest number which has not appeared is 5191516. - Benjamin Chaffin, Oct 09 2016

REFERENCES

Suggested by J. C. Lagarias.

LINKS

Nick Hobson, Table of n, a(n) for n=1..10000

Nick Hobson, Python program for this sequence

Index entries for sequences related to Recamán's sequence

Index entries for sequences that are permutations of the natural numbers

MAPLE

h := array(1..100000); maxt := 100000; a := array(1..1000); a[1] := 1; h[1] := 1; for nx from 2 to 1000 do for i from 0 to 100 do t1 := a[nx-1]-nx-i; if t1>0 and h[t1] <> 1 then a[nx] := t1; if t1 < maxt then h[t1] := 1; fi; break; fi; t1 := a[nx-1]+nx+i; if h[t1] <> 1 then a[nx] := t1; if t1 < maxt then h[t1] := 1; fi; break; fi; od; od; evalm(a);

MATHEMATICA

h[1] = 1; h[_] = 0; maxt = 100000; a[1] = 1; a[_] = 0; For[nx = 2, nx <= 1000, nx++, For[i = 0, i <= 100, i++, t1 = a[nx - 1] - nx - i; If[t1 > 0 && h[t1] != 1, a[nx] = t1; If[t1 < maxt, h[t1] = 1]; Break[]]; t1 = a[nx - 1] + nx + i; If[h[t1] != 1, a[nx] = t1; If[t1 < maxt, h[t1] = 1]; Break[]]]]; Table[a[n], {n, 1, 100}](* Jean-François Alcover, May 09 2012, after Maple *)

PROG

(PARI) A064389(n=1000, show=0)={ my(k, s, t); for(n=1, n, k=n; while( !(t>k && !bittest(s, t-k) && t-=k) && !(!bittest(s, t+k)  && t+=k), k++); s=bitor(s, 1<<t); show&&print1(t", ")); t} \\ M. F. Hasler, Nov 03 2014

CROSSREFS

Cf. A005132, A046901, A064387, A064388. Agrees with A064387 for first 187 terms, then diverges.

Sequence in context: A005132 A064388 A064387 * A118201 A274647 A113880

Adjacent sequences:  A064386 A064387 A064388 * A064390 A064391 A064392

KEYWORD

nonn,easy,look,nice

AUTHOR

N. J. A. Sloane, Sep 28 2001

STATUS

approved

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Last modified August 20 01:56 EDT 2017. Contains 290821 sequences.