A119802 a(1) = 1. For m >= 0 and 1 <= k <= 2^m, a(2^m +k) = number of earlier terms of the sequence which equal a(k).

1, 1, 2, 2, 2, 2, 4, 4, 2, 2, 6, 6, 6, 6, 2, 2, 2, 2, 10, 10, 10, 10, 2, 2, 12, 12, 4, 4, 4, 4, 12, 12, 2, 2, 14, 14, 14, 14, 6, 6, 14, 14, 6, 7, 7, 7, 14, 14, 14, 14, 4, 4, 4, 4, 14, 14, 4, 4, 12, 12, 12, 12, 8, 8, 2, 2, 16, 16, 16, 16, 12, 12, 16, 16, 7, 7, 7, 7, 16, 16, 16, 16, 4, 4, 4, 4

Offset: 1

Author

Leroy Quet, May 24 2006

Keywords

• easy
• nonn

Comments

Interpreted as a triangle with row lengths A011782, row m+1 is the frequency of each term in rows 1..m among terms in the sequence thus far (including the part of row m+1 itself thus far). - Neal Gersh Tolunsky, Oct 03 2023

Examples

			8 = 2^2 + 4; so for a(8) we want the number of terms among terms a(1), a(2),... a(7) which equal a(4) = 2. So a(8) = 4.
As a triangle:
      k=1  2   3   4   5   6  7  8 ...
  m=1:  1;
  m=2:  1;
  m=3:  2, 2;
  m=4:  2, 2,  4,  4;
  m=5:  2, 2,  6,  6,  6,  6, 2, 2;
  m=6:  2, 2, 10, 10, 10, 10, 2, 2, 12, 12, 4, 4, 4, 4, 12, 12;
  ...
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
• Neal Gersh Tolunsky, Run length transform of 2^16 terms

Crossrefs

Cf. A119803, A011782 (row lengths), A365882.

Programs

PARI

A119802(mmax)= { local(a,ncopr); a=[1]; for(m=0,mmax, for(k=1,2^m, ncopr=0; for(i=1,2^m+k-1, if( a[i]==a[k], ncopr++; ); ); a=concat(a,ncopr); ); ); return(a); }
print(A119802(6)); \\ R. J. Mathar, May 30 2006

Extensions

More terms from R. J. Mathar, May 30 2006