A046901 a(n) = a(n-1) - n if a(n-1) > n, else a(n) = a(n-1) + n.

1, 3, 6, 2, 7, 1, 8, 16, 7, 17, 6, 18, 5, 19, 4, 20, 3, 21, 2, 22, 1, 23, 46, 22, 47, 21, 48, 20, 49, 19, 50, 18, 51, 17, 52, 16, 53, 15, 54, 14, 55, 13, 56, 12, 57, 11, 58, 10, 59, 9, 60, 8, 61, 7, 62, 6, 63, 5, 64, 4, 65, 3, 66, 2, 67, 1, 68, 136, 67, 137

Offset: 1

Author

N. J. A. Sloane

Keywords

• easy
• nonn
• nice
• look

Comments

Variation (1) on Recamán's sequence A005132.

a(A134931(n-1)) = 1. - Reinhard Zumkeller, Jan 31 2013

Links

• N. J. A. Sloane, First 10000 terms
• Nick Hobson, Python program for this sequence
• Kival Ngaokrajang, scatter plot in log-log scale looks, for both this sequence and A211346.
• Index entries for sequences related to Recamán's sequence

Crossrefs

Cf. A008343, A008344, A005132.

Cf. A076039, A003462, A076041, A076042, A057198.

Cf. A085059.

Cf. A238324.

Programs

Haskell

a046901 n = a046901_list !! (n-1)
a046901_list = scanl1 (\u v -> if u > v then u - v else u + v) [1..]
-- Reinhard Zumkeller, Dec 07 2015, Jan 31 2013

Maple

A046901 := proc(n) option remember; if n = 1 then 1 else if A046901(n-1)>n then A046901(n-1)-n else A046901(n-1)+n; fi; fi; end;

Mathematica

a[1]=1;a[n_]:=a[n]=If[a[n-1]>n,a[n-1]-n,a[n-1]+n]; Table[a[i],{i,70}]  (* Harvey P. Dale, Apr 01 2011 *)
nxt[{n_,a_}]:={n+1,If[a>n+1,a-n-1,a+n+1]}; NestList[nxt,{1,1},70][[All,2]] (* Harvey P. Dale, Jun 01 2019 *)

PARI

a(n)=if(n<2,1,a(n-1)-if(sign(n-a(n-1))+1,-1,1)*n);

Formula

This is a concatenation S_0, S_1, S_2, ... where S_i = [b_0, b_1, ..., b_{k-1}], k=5*3^i, with b_0 = 1, b_{2j} = k+j, b_{2j+1} = (k+1)/2-j. E.g., S_0 = [1, 3, 6, 2, 7].

For any m>=1, for k such that 5*3^k+3>12m, a((5*3^k+3-12*m)/6)= m. For example, for k>=1, a((5*3^k-9)/6) = 1. - Benoit Cloitre, Oct 31 2002

a(n) = A008343(n+1) + 1. - Jon Maiga, Jul 09 2021