A065120 Highest power of 2 dividing A057335(n).

0, 1, 2, 1, 3, 2, 1, 1, 4, 3, 2, 2, 1, 1, 1, 1, 5, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 5, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 6, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,3

Comments

a(n) appears on row 1 of the array illustrated in A066099.

Except for initial zero, ordinal transform of A062050. After initial zero, n-th chunk consists of n, one n-1, two (n-2)'s, ..., 2^(k-1) (n-k)'s, ..., 2^(n-1) 1's. - Franklin T. Adams-Watters, Sep 11 2006

Zero together with a triangle read by rows in which row j lists the first 2^(j-1) terms of A001511 in nonincreasing order, j >= 1, see example. Also row j lists the first parts, in nonincreasing order, of the compositions of j. - Omar E. Pol, Sep 11 2013

The n-th row represents the frequency distribution of 1, 2, 3, ..., 2^(n-1) in the first 2^n - 1 terms of A003602. - Gary W. Adamson, Jun 10 2021

Links

Table of n, a(n) for n=0..105.

Formula

From Daniel Starodubtsev, Aug 05 2021: (Start)

a(n) = A001511(A059894(n) - 2^A000523(n) + 1) for n > 0 with a(0) = 0.

a(2n+1) = a(n), a(2n) = a(n) + A036987(n-1) for n > 1 with a(0) = 0, a(1) = 1. (End)

Example

A057335(7)= 30 and 30 = 2*3*5 so a(7) = 1; A057335(9)= 24 and 24 = 8*3 so a(9) = 3
From Omar E. Pol, Aug 30 2013: (Start)
Written as an irregular triangle with row lengths A011782:
  0;
  1;
  2,1;
  3,2,1,1;
  4,3,2,2,1,1,1,1;
  5,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1;
  6,5,4,4,3,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;
  ...
Column 1 is A001477. Row sums give A000225. Row lengths is A011782.
(End)

Mathematica

nmax = 105;
A062050 = Flatten[Table[Range[2^n], {n, 0, Log[2, nmax] // Ceiling}]];
Module[{b}, b[_] = 0;
a[n_] := If[n == 0, 0, With[{t = A062050[[n]]}, b[t] = b[t] + 1]]];
a /@ Range[0, nmax] (* Jean-François Alcover, Jan 12 2022 *)

Prog

(PARI) lista(nn) = {my(v = vector(nn)); v[1] = 1; for (i=2, nn, v[i] = mg(i-1)*v[(i+1)\2]; ); for (i=1, nn, print1(valuation(v[i], 2), ", "); ); } \\ Michel Marcus, Feb 09 2014
(PARI) my(L(n)=if(n, logint(n, 2), -1)); a(n) = my(p=L(n)); p - L(n-1<<p); \\ Kevin Ryde, Aug 06 2021

Crossrefs

Cf. A066099, A062050, A011782.

Cf. A003602.

Sequence in context: A334749 A266640 A359350 * A176206 A232890 A300441

Adjacent sequences: A065117 A065118 A065119 * A065121 A065122 A065123

Keyword

easy,nonn

Author

Alford Arnold, Nov 12 2001

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003

Status

approved