A237451 - OEIS

%I #17 Nov 05 2024 03:12:03

%S 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,

%T 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,

%U 1,2,3,4,5,0,1,2,3,4,5,0,1,2,3,4,5,0,1,2,3,4,5

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

%C 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).

%C A237452 gives the corresponding row index.

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

%H Antti Karttunen, <a href="/A237451/b237451.txt">Table of squares with sizes 1x1 .. 30x30, flattened</a>

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

%F a(n) = A121997(n)-1. - _M. F. Hasler_, Feb 16 2014

%e This irregular table begins as:

%e 0;

%e 0,1;

%e 0,1;

%e 0,1,2;

%e 0,1,2;

%e 0,1,2;

%e 0,1,2,3;

%e 0,1,2,3;

%e 0,1,2,3;

%e 0,1,2,3;

%e 0,1,2,3,4;

%e 0,1,2,3,4;

%e 0,1,2,3,4;

%e 0,1,2,3,4;

%e 0,1,2,3,4;...

%o (Scheme) (define (A237451 n) (modulo (-1+ (A064866 n)) (A074279 n)))

%o (Python)

%o from sympy import integer_nthroot

%o 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

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

%K nonn,tabf,easy

%O 1,8

%A _Antti Karttunen_, Feb 08 2014