A242926 -id:A242926 - cp's OEIS frontend

A242947 a(n) = n / A242926(n-1).

1, 2, 3, 2, 5, 1, 7, 2, 3, 2, 11, 3, 13, 2, 1, 2, 17, 1, 19, 2, 1, 2, 23, 1, 5, 2, 3, 2, 29, 1, 31, 2, 3, 2, 1, 3, 37, 2, 1, 2, 41, 1, 43, 2, 5, 2, 47, 1, 7, 2, 3, 2, 53, 1, 1, 2, 3, 2, 59, 3, 61, 2

Offset: 1

Paul Curtz, May 27 2014

nonn

a(n) = n: A008578.
a(2n) = 2, 2, 1, 2, 2, 3, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 3,... .
A242926 is the denominator of a super autosequence based on 1/n. See A189731 and A242563.

			a(1)=1/1, a(2)=2/1=2, a(3)=3/1=3, a(4)=4/2=2, a(5)=5/1=5, a(6)=6/6=1, a(7)=7/1=7, a(8)=8/4=2, ... .

Cf. A242926, A008578, A189731, A242563.

Edited by N. J. A. Sloane, Jun 12 2014

A189731 a(n) = numerator of B(0,n) where B(n,n) = 0, B(n-1,n) = 1/n, and B(m,n) = B(m-1,n+1) - B(m-1,n).

Original entry on oeis.org

0, 1, 1, 3, 2, 17, 4, 23, 25, 61, 18, 107, 40, 421, 1363, 1103, 210, 5777, 492, 7563, 24475, 19801, 2786, 103681, 33552, 135721, 146401, 355323, 39650, 1860497, 97108, 2435423, 2627065, 6376021, 20633238, 11128427, 1459960, 43701901

Offset: 0

Paul Curtz, Apr 26 2011

Square array B(m,n) begins:
    0,    1/1,   1/1,   3/2,   2/1,  17/6,  ...
   1/1,    0,    1/2,   1/2,   5/6,   7/6,  ...
  -1/1,   1/2,    0,    1/3,   1/3,   7/12, ...
   3/2,  -1/2,   1/3,    0,    1/4,   1/4,  ...
  -2/1,   5/6,  -1/3,   1/4,    0,    1/5,  ...
  17/6,  -7/6,   7/12, -1/4,   1/5,    0,   ...
The inverse binomial transform of B(0,n) gives B(n,0) and thus it is an eigensequence in the sense that it remains the same (up to a sign) under inverse binomial transform.
The bisection of B(0,n) (odd part) gives A175385/A175386, and thus a(2*n+1) = A175385(n+1).

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A000204, A242926 (denominators).

Cf. A174341, A177690, A181722.

B:= proc(m, n) option remember;
      if m=n then 0
    elif n=m+1 then 1/n
    elif n>m then B(m, n-1) +B(m+1, n-1)
    else B(m-1, n+1) -B(m-1, n)
      fi
    end:
a:= n-> numer(B(0, n)):
seq(a(n), n=0..50);  # Alois P. Heinz, Apr 29 2011

Rest[Numerator[Abs[CoefficientList[Normal[Series[Log[1 - x^2/(1 + x)], {x, 0, 40}]], x]]]] (* Vaclav Kotesovec, Jul 07 2020 *)
Table[Numerator[(LucasL[n]-1)/n],{n,1,38}] (* Artur Jasinski, Oct 21 2022 *)

Numerator of (A000204(n) - 1)/n. - Artur Jasinski, Oct 21 2022

cp's OEIS Frontend

A242947 a(n) = n / A242926(n-1).

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A189731 a(n) = numerator of B(0,n) where B(n,n) = 0, B(n-1,n) = 1/n, and B(m,n) = B(m-1,n+1) - B(m-1,n).

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