A237451 Zero-based column index to irregular tables organized as successively larger square matrices.

0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5

Offset

1,8

Comments

With sequences constructed of successively larger square matrices (cf. A074279), a(n) will return the distance of n from the left edge of the matrix that n is located in, with 0 standing for the leftmost column (please see the Example section).

A237452 gives the corresponding row index.

A238013 and A121997 give these same row and column indices, starting the numbering with index 1. - M. F. Hasler, Feb 17 2014

Links

Antti Karttunen, Table of squares with sizes 1x1 .. 30x30, flattened

Formula

a(n) = (A064866(n)-1) modulo A074279(n).

a(n) = A121997(n)-1. - M. F. Hasler, Feb 16 2014

Example

This irregular table begins as:
0;
0,1;
0,1;
0,1,2;
0,1,2;
0,1,2;
0,1,2,3;
0,1,2,3;
0,1,2,3;
0,1,2,3;
0,1,2,3,4;
0,1,2,3,4;
0,1,2,3,4;
0,1,2,3,4;
0,1,2,3,4;...

Prog

(Scheme) (define (A237451 n) (modulo (-1+ (A064866 n)) (A074279 n)))
(Python)
from sympy import integer_nthroot
def A237451(n): return (n-(k:=(m:=integer_nthroot(3*n, 3)[0])+(6*n>m*(m+1)*((m<<1)+1)))*(k-1)*((k<<1)-1)//6-1)%k # Chai Wah Wu, Nov 04 2024

Crossrefs

Cf. A002262, A064866, A074279, A237452, A237265.

Sequence in context: A220663 A220659 A025858 * A215592 A025684 A025678

Adjacent sequences: A237448 A237449 A237450 * A237452 A237453 A237454

Keyword

nonn,tabf,easy

Author

Antti Karttunen, Feb 08 2014

Status

approved