A008344 a(1)=0; thereafter a(n+1) = a(n) - n if a(n) >= n otherwise a(n+1) = a(n) + n.

0, 1, 3, 0, 4, 9, 3, 10, 2, 11, 1, 12, 0, 13, 27, 12, 28, 11, 29, 10, 30, 9, 31, 8, 32, 7, 33, 6, 34, 5, 35, 4, 36, 3, 37, 2, 38, 1, 39, 0, 40, 81, 39, 82, 38, 83, 37, 84, 36, 85, 35, 86, 34, 87, 33, 88, 32, 89, 31, 90, 30, 91, 29, 92, 28, 93, 27, 94, 26, 95, 25, 96, 24, 97, 23, 98

Offset

1,3

Comments

p^a(n) = A084110(p^(n-1)) for n>1 and p prime. - Reinhard Zumkeller, May 12 2003

For n > 1: a(A029858(n)) = A029858(n) and a(A003462(n)) = 0. - Reinhard Zumkeller, May 09 2012

Absolute first differences of A085059; abs(a(n+1)-a(n)) = n, see also A086283. - Reinhard Zumkeller, Oct 17 2014

For n>3, when a(n) = 3, a(n+1) is in A116970. - Bill McEachen, Oct 03 2023

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..29524 (Up to the 10th 0 term)

Index entries for sequences related to Recamán's sequence

Formula

This is a concatenation S_0, S_1, S_2, ... where S_i = [b_0, b_1, ..., b_{3^(i+1)-1}] with b_0 = 0, b_{2j-1} = k+1-j, b_{2j} = 2k+j (j=1..k), k=(3^(i+1)-1)/2. E.g. S_0 = [0, 1, 3], S_1 = [0, 4, 9, 3, 10, 2, 11, 1, 12].

a((3^n-1)/2) = 0; a((3^n-1)/2 + 2k-1) = (3^n+1)/2 - k for 1 <= k <= (3^n-1)/2; a((3^n-1)/2 + 2k) = 3^n - 1 + k for 1 <= k < (3^n-1)/2. - Benoit Cloitre, Jan 09 2003 [Corrected by Jianing Song, May 25 2021]

a(n) = (n-1+a(n-1)) mod (2*(n-1)). - Jon Maiga, Jul 09 2021

Maple

A008344 := proc(n) option remember; if n = 0 then 0 elif A008344(n-1) >= (n-1) then A008344(n-1)-(n-1) else A008344(n-1)+(n-1); fi; end;

Mathematica

a[1]=0; a[n_] := a[n]=If[a[n-1]>=n-1, a[n-1]-n+1, a[n-1]+n-1]
Transpose[ NestList[ If[First[#]>=Last[#], {First[#]-Last[#], Last[#]+1}, {First[#]+Last[#], Last[#]+1}]&, {0, 1}, 80]][[1]] (* Harvey P. Dale, Jun 20 2011 *)
s = 0; Table[If[s < n, s = s + n, s = s - n], {n, 0, 80}] (* Horst H. Manninger, Dec 03 2018 *)

Prog

(Haskell)
a008344 n = a008344_list !! (n-1)
a008344_list = 0 : f 0 [1..] where
   f x (z:zs) = y : f y zs where y = if x < z then x + z else x - z
-- Reinhard Zumkeller, Oct 17 2014, May 08 2012
(PARI) a(n) = my(expo = logint(2*n+1, 3), res = n - (3^expo-1)/2); if(res==0, 0, if(res%2, (3^expo-res)/2, 3^expo-1+res/2)) \\ Jianing Song, May 25 2021

Crossrefs

Cf. A046901, A008343, A088230, A085059, A086283.

Equals A085059(n)-1.

Cf. A076042 (based on squares).

Sequence in context: A255504 A178593 A021332 * A088230 A181482 A330420

Adjacent sequences: A008341 A008342 A008343 * A008345 A008346 A008347

Keyword

nonn,easy,nice,look

Author

N. J. A. Sloane

Extensions

Name edited by Dmitry Kamenetsky, Feb 14 2017

Status

approved