0,3

The name "Recaman's sequence" is due to N. J. A. Sloane (njas(AT)research.att.com), not the author!

I conjecture that every number eventually appears - see A057167, A064227, A064228. - N. J. A. Sloane (njas(AT)research.att.com).

Comment from David Wilson (dwilson(AT)gambitcomm.com), Jul 13 2009: (Start) The sequence satisfies [1] a(n) >= 0, [2] |a(n)-a(n-1)| = n, and tries to avoid repeats by greedy choice of a(n) = a(n-1) -+ n.

This "wants" to be an injection on N = {0, 1, 2, ...}, as it attempts to avoid repeats by choice of a(n) = a(n-1) + n when a(n) = a(n-1) - n is a repeat.

Clearly, there are injections satisfying [1] and [2], e.g, a(n) = n(n+1)/2.

Is there a lexicographically smallest injection satisfying [1] and [2]? (End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

N. J. A. Sloane, The first 100000 terms

GBnums, See: A nice OEIS sequence

Nick Hobson, Python program for this sequence

C. L. Mallows, Plot (jpeg) of first 10000 terms

C. L. Mallows, Plot (postscript) of first 10000 terms

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 Recaman's sequence

Consider n=6. We have a(5)=7 and try to subtract 6. The result, 1, is certainly positive, but we cannot use it because 1 is already in the sequence. So we must add 6 instead, getting a(6) = 7 + 6 = 13.

h := array(1..100000); maxt := 100000; a := [1]; ad := [1]; su := []; h[1] := 1; for nx from 2 to 500 do t1 := a[nx-1]-nx; if t1>0 and h[t1] <> 1 then su := [op(su), nx]; else t1 := a[nx-1]+nx; ad := [op(ad), nx]; fi; a := [op(a), t1]; if t1 <= maxt then h[t1] := 1; fi; od: # a is A005132, ad is A057165, su is A057166

a = {1}; Do[ If[ a[ [ -1 ] ] - n > 0 && Position[ a, a[ [ -1 ] ] - n ] == {}, a = Append[ a, a[ [ -1 ] ] - n ], a = Append[ a, a[ [ -1 ] ] + n ] ], {n, 2, 70} ]; a

f[s_List] := Block[{a = s[[ -1]], len = Length@s}, Append[s, If[a > len && !MemberQ[s, a - len], a - len, a + len]]]; Nest[f, {0}, 70] [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 01 2009]

(PARI) a(n)=if(n<2, 1, if(abs(sign(a(n-1)-n)-1)+setsearch(Set(vector(n-1, i, a(i))), a(n-1)-n), a(n-1)+n, a(n-1)-n)) (from Benoit Cloitre)

A005132( nMax=10^3 )={ local( s, t ); for( n=1, nMax, print1( t += if( t<=n | bittest( s, t-n ), n, -n), ", "); s=bitor( s, 1<<t))} (from M. F. Hasler, May 11 2008)

Cf. A057165 (addition steps), A057166 (subtraction steps), A057167 (steps to hit n), A008336, A046901 (simplified version), A063733.

Cf. A064227 (records for reaching n), A064228 (n's that take a record number of steps to reach), A064284 (no. of times n appears), A064288, A064289, A064290 (heights of terms).

Cf. A064291 (record highs), A064387, A064388, A064389 (further variants).

A row of A066201.

Condensed version: A119632.

Sequence in context: A065232 A074170 A076543 this_sequence A064388 A064387 A064389

Adjacent sequences: A005129 A005130 A005131 this_sequence A005133 A005134 A005135

easy,nonn,nice

B. Recaman [Recam\'{a}n], N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

Allan Wilks (allan(AT)research.att.com), Nov 06, 2001, computed 10^15 terms of this sequence. At this point the smallest missing number is 852655.

After 10^25 terms of A005132 the smallest missing number is still 852655. - Benjamin Chaffin (chaffin(AT)gmail.com), Jun 13 2006

Even after 7.78*10^37 terms, the smallest missing number is still 852655. - Benjamin Chaffin (chaffin(AT)gmail.com), Mar 28 2008