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 A064388 Variation (3) on Recamán's sequence (A005132): set s (the step size) initially equal to 2; to get a(n), we first try to subtract s from a(n-1): a(n) = a(n-1)-s if positive and not already in the sequence, in which case we change s to s+1; if not, a(n) = a(n-1)+s+i, where i >= 0 is the smallest number such that a(n-1)+s+i has not already appeared and now we change s to s+i+1 4

%I

%S 1,3,6,2,7,13,20,12,21,11,22,10,23,9,24,8,25,43,62,42,63,41,18,44,17,

%T 45,16,46,15,47,14,48,83,119,82,120,81,121,80,38,84,37,85,36,86,35,87,

%U 34,88,33,89,32,90,31,91,30,92,29,93,28,94,27,95,26,96,167,239,166,240

%N Variation (3) on Recamán's sequence (A005132): set s (the step size) initially equal to 2; to get a(n), we first try to subtract s from a(n-1): a(n) = a(n-1)-s if positive and not already in the sequence, in which case we change s to s+1; if not, a(n) = a(n-1)+s+i, where i >= 0 is the smallest number such that a(n-1)+s+i has not already appeared and now we change s to s+i+1

%C Variation (4) (A064389) is the nicest of these variations.

%C I would also like to get the following sequences: number of steps before n appears (or 0 if n never appears), list of numbers that never appear, height of n (cf. A064288, A064289, A064290), etc.

%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>

%o (BASIC)

%o rem Chipmunk BASIC v3.6.4(b8) http://www.nicholson.com/rhn/basic/

%o max=1000 : dim a(max)

%o s=2 : z=1 : a(z)=1 : print str\$(z)+",";

%o for n=1 to 200

%o x=z-s : if x <= 0 then goto yyy

%o if a(x)=0 then a(x)=1 : print str\$(x)+","; : s=s+1 : z=x : goto xxx

%o yyy: for i=0 to max

%o x=z+s+i

%o if a(x)=0 then a(x)=1 : print str\$(x)+","; : s=s+i+1 : z=x : goto xxx

%o next i

%o xxx: next n

%o print : end

%o rem _Jeremy Gardiner_, Feb 22 2014

%Y Cf. A005132, A046901, A064387, A064389.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Sep 28 2001

%E More terms from _David Wasserman_, Jul 16 2002

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Last modified November 20 06:06 EST 2018. Contains 317385 sequences. (Running on oeis4.)