A070989 -id:A070989 - cp's OEIS frontend

A246435 Length of representation of n in fractional base 3/2.

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9

Offset: 0

Reinhard Zumkeller, Sep 05 2014

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
B. Chen, R. Chen, J. Guo, S. Lee et al., On Base 3/2 and its sequences, arXiv:1808.04304 [math.NT], 2018.
Index entries for sequences related to fractional bases.

Cf. A024629, A055642, A070989, A081604, A081848 (run lengths), A244040.

a246435 n = if n < 3 then 1 else a246435 (2 * div n 3) + 1
-- Reinhard Zumkeller, Sep 05 2014

a[n_] := If[n < 3, 1, a[2 Quotient[n, 3]] + 1]; Array[a, 100, 0] (* Jean-François Alcover, Feb 05 2019 *)

a(n) = if(n < 3, 1, a(n\3 * 2) + 1); \\ Amiram Eldar, Jul 30 2025

a(n) = if n < 3 then 1, otherwise a(2*floor(n/3)) + 1.

a(n) = A055642(A024629(n)).

A076588 First occurrence of n as a term in the continued fraction for Pi/4.

Original entry on oeis.org

2, 8, 3, 76, 17, 67, 50, 54, 11, 20, 73, 413, 59, 162, 7, 75, 13, 587, 393, 24, 112, 228, 403, 40, 843, 560, 590, 69, 187, 617, 215, 400, 1182, 259, 1680, 548, 758, 226, 133, 78, 1265, 589, 96, 169, 3108, 5892, 258, 261, 4608, 3810, 2386, 1251, 2698, 2374

Offset: 1

Benoit Cloitre, Oct 20 2002

Cf. A032523, A070989.

With[{cf=ContinuedFraction[Pi/4,6000]},Table[Position[cf,n,1,1],{n,60}]]//Flatten (* Harvey P. Dale, Aug 25 2025 *)

\\ 15000 precision digits
v=contfrac(Pi/4); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)

cp's OEIS Frontend

A246435 Length of representation of n in fractional base 3/2.

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