A088230 -id:A088230 - cp's OEIS frontend

A088337 Self-inverse integer permutation induced by A088230.

3, 10, 6, 0, 27, 17, 2, 15, 556, 13, 1, 68, 44, 9, 42, 7, 40, 5, 38, 72, 36, 74, 34, 76, 32, 78, 30, 4, 179, 121, 26, 119, 24, 117, 22, 115, 20, 113, 18, 111, 16, 109, 14, 107, 12, 105, 542, 103, 187, 101, 189, 99, 191, 97, 193, 95, 195, 93, 197, 91, 199, 89, 201, 87

Offset: 0

Reinhard Zumkeller, Nov 07 2003

nonn

A088230(a(n))=A088230(n): all nonnegative numbers occur exactly twice in A088230, a(n) gives the position of the other occurrence of A088230(n).

Index entries for sequences that are permutations of the natural numbers

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

Original entry on oeis.org

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

N. J. A. Sloane

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

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

Cf. A046901, A008343, A088230, A085059, A086283.
Equals A085059(n)-1.
Cf. A076042 (based on squares).

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

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;

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 *)

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

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

Name edited by Dmitry Kamenetsky, Feb 14 2017

cp's OEIS Frontend

A088337 Self-inverse integer permutation induced by A088230.

Views

Author

Keywords

Comments

Links

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Formula

Extensions