A026182 -id:A026182 - cp's OEIS frontend

A026183 Position of n in A026182.

1, 2, 5, 3, 4, 11, 13, 6, 17, 7, 8, 23, 9, 10, 29, 31, 12, 35, 37, 14, 41, 15, 16, 47, 49, 18, 53, 19, 20, 59, 21, 22, 65, 67, 24, 71, 25, 26, 77, 27, 28, 83, 85, 30, 89, 91, 32, 95, 33, 34, 101, 103, 36, 107, 109, 38, 113, 39, 40, 119, 121

Offset: 1

Clark Kimberling

nonn

Also position of n in A026198.

F. M. Dekking, Permutations of N generated by left-right filling algorithms, arXiv:2001.08915 [math.CO], 2020.

Cf. A026182, A026198.

Edited by N. J. A. Sloane, Jan 31 2020

A026198 Duplicate of A026182.

Original entry on oeis.org

1, 2, 4, 5, 3, 8, 10, 11, 13, 14, 6, 17, 7, 20, 22, 23, 9, 26, 28, 29, 31, 32, 12, 35, 37, 38, 40, 41, 15, 44, 16, 47, 49, 50, 18, 53, 19, 56, 58, 59, 21, 62, 64, 65, 67, 68, 24, 71, 25, 74, 76, 77, 27, 80, 82, 83, 85, 86, 30, 89, 91, 92, 94

Offset: 1

dead

A026206 Duplicate of A026182.

Original entry on oeis.org

1, 2, 4, 5, 3, 8, 10, 11, 13, 14, 6, 17, 7, 20, 22, 23, 9, 26, 28, 29, 31, 32, 12, 35, 37, 38, 40, 41, 15, 44, 16, 47, 49, 50, 18, 53, 19, 56, 58, 59, 21, 62, 64, 65, 67, 68, 24, 71, 25, 74, 76, 77, 27, 80, 82, 83, 85, 86, 30, 89, 91, 92, 94

Offset: 1

dead

A026166 For n >= 2, let h=floor((n-1)/2), L=n-h, R=n+h; then a(L)=n if a(L) not yet defined, otherwise a(R)=n; thus |a(n)-n| = floor((1/2)*(a(n)-1)).

Original entry on oeis.org

1, 2, 4, 3, 8, 10, 5, 6, 16, 7, 20, 22, 9, 26, 28, 11, 12, 34, 13, 14, 40, 15, 44, 46, 17, 18, 52, 19, 56, 58, 21, 62, 64, 23, 24, 70, 25, 74, 76, 27, 80, 82, 29, 30, 88, 31, 32, 94, 33, 98, 100, 35, 36, 106, 37, 38, 112, 39, 116, 118, 41, 42

Offset: 1

Clark Kimberling

nonn

Every positive integer occurs exactly once. The inverse permutation of the positive integers is given by A026167. - Clark Kimberling, Oct 20 2019

Clark Kimberling, Table of n, a(n) for n = 1..10000 (terms 1..1502 from R. J. Mathar)
F. M. Dekking, Permutations of N generated by left-right filling algorithms, arXiv:2001.08915 [math.CO], 2020.

Cf. A026167, A026182, A026198, A026202.

a[1] = 1; z = 300;
Do[{L, R} = {n - #, n + #} &[Floor[(n - 1)/2]];
  If[! Head[a[L]] === Integer, a[L] = n, a[R] = n], {n, 2, z}];
a026166 = Most[Last[
   Last[Reap[NestWhile[# + 1 &, 1, Head[Sow[a[#]]] === Integer &]]]]];
ListPlot[a026166]  (* Peter J. C. Moses, Oct 20 2019 *)

seq(n)={my(a=vector(n)); a[1]=1; for(i=1, 2*n-1, my(h=(i-1)\2); if(!a[i-h], a[i-h]=i, if(i+h<=n, a[i+h]=i))); a} \\ Andrew Howroyd, Oct 15 2019

A026166 = {1: 1}
for n in range(2, 1000):
    h=(n-1)//2
    L=n-h
    R=n+h
    if not L in A026166 :
        A026166[L]=n
    else :
        A026166[R]=n
for n in range(1,2000):
    if n in A026166:
       print(A026166[n], end=',')
    else:
        break
# R. J. Mathar, Aug 26 2019

|a(n)-n| = floor((1/2)*(a(n)-1)).

This formula does not permit us to calculate the n-th term of the sequence, since the equation |x-n| = floor((1/2)*(x-1)) has at least 2 integer solutions for all n. - Michel Dekking, Nov 26 2019

Edited by N. J. A. Sloane, Jan 31 2020

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A026183 Position of n in A026182.

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A026198 Duplicate of A026182.

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A026206 Duplicate of A026182.

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A026166 For n >= 2, let h=floor((n-1)/2), L=n-h, R=n+h; then a(L)=n if a(L) not yet defined, otherwise a(R)=n; thus |a(n)-n| = floor((1/2)*(a(n)-1)).

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