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.

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, 45, 16, 46, 15, 47, 14, 48, 83, 119, 82, 120, 81, 121, 80, 38, 84, 37, 85, 36, 86, 35, 87, 34, 88, 33, 89, 32, 90, 31, 91, 30, 92, 29, 93, 28, 94, 27, 95, 26, 96, 167, 239, 166, 240

Offset: 1

Author

N. J. A. Sloane, Sep 28 2001

Keywords

• nonn
• easy

Comments

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

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.

Links

• Index entries for sequences related to Recamán's sequence

Crossrefs

Cf. A005132, A046901, A064387, A064389.

Programs

BASIC

rem Chipmunk BASIC v3.6.4(b8) http://www.nicholson.com/rhn/basic/
max=1000 : dim a(max)
s=2 : z=1 : a(z)=1 : print str$(z)+",";
for n=1 to 200
x=z-s : if x <= 0 then goto yyy
if a(x)=0 then a(x)=1 : print str$(x)+","; : s=s+1 : z=x : goto xxx
yyy: for i=0 to max
x=z+s+i
if a(x)=0 then a(x)=1 : print str$(x)+","; : s=s+i+1 : z=x : goto xxx
next i
xxx: next n
print : end
rem Jeremy Gardiner, Feb 22 2014

Extensions

More terms from David Wasserman, Jul 16 2002