cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A367055 Triangle read by rows: T(n, k) = A000120(n) + A000120(k), 0 <= k <= n.

Original entry on oeis.org

0, 1, 2, 1, 2, 2, 2, 3, 3, 4, 1, 2, 2, 3, 2, 2, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3
Offset: 0

Views

Author

Mithra Karamchedu and Sophia Pi, Nov 03 2023

Keywords

Comments

T(n, k) is the sum of the Hamming weight of n and the Hamming weight of k.
See A365618 for a table read by antidiagonals.

Examples

			Triangle begins:
      k=0  1  2  3  4  5
  n=0:  0;
  n=1:  1, 2;
  n=2:  1, 2, 2;
  n=3:  2, 3, 3, 4;
  n=4:  1, 2, 2, 3, 2;
  n=5:  2, 3, 3, 4, 3, 4;
        ...
		

Crossrefs

Programs

  • Mathematica
    T[n_, k_] := DigitCount[n, 2, 1] + DigitCount[k, 2, 1]
  • Python
    from math import comb, isqrt
    def A367055(n): return (n-comb(r:=(m:=isqrt(k:=n+1<<1))+(k>m*(m+1)),2)).bit_count()+(r-1).bit_count() # Chai Wah Wu, Nov 11 2024

Formula

T(n, k) = A000120(n) + A000120(k).