A371101 Array A read by upward antidiagonals in which the entry A(n,k) = A371092(A371100(n, k)), n,k >= 1.

1, 1, 3, 1, 2, 3, 1, 3, 1, 6, 1, 2, 3, 5, 2, 1, 3, 1, 6, 4, 9, 1, 2, 3, 5, 2, 8, 6, 1, 3, 1, 6, 4, 9, 2, 12, 1, 2, 3, 5, 2, 8, 6, 11, 1, 1, 3, 1, 6, 4, 9, 2, 12, 7, 15, 1, 2, 3, 5, 2, 8, 6, 11, 1, 14, 9, 1, 3, 1, 6, 4, 9, 2, 12, 7, 15, 4, 18, 1, 2, 3, 5, 2, 8, 6, 11, 1, 14, 9, 17, 5, 1, 3, 1, 6, 4, 9, 2, 12, 7, 15, 4, 18, 10, 21

Offset: 1

Author

Antti Karttunen, Apr 19 2024

Keywords

• nonn
• tabl

Comments

A(n, k) gives the column index of A371100(n, k) in array A257852.

Examples

			The array begins:
n\k|  1  2  3  4  5  6  7   8  9  10 11  12  13  14  15  16  17  18
---+--------------------------------------------------------------------
1  |  1, 3, 3, 6, 2, 9, 6, 12, 1, 15, 9, 18,  5, 21, 12, 24,  4, 27, ...
2  |  1, 2, 1, 5, 4, 8, 2, 11, 7, 14, 4, 17, 10, 20,  1, 23, 13, 26, ...
3  |  1, 3, 3, 6, 2, 9, 6, 12, 1, 15, 9, 18,  5, 21, 12, 24,  4, 27, ...
4  |  1, 2, 1, 5, 4, 8, 2, 11, 7, 14, 4, 17, 10, 20,  1, 23, 13, 26, ...
5  |  1, 3, 3, 6, 2, 9, 6, 12, 1, 15, 9, 18,  5, 21, 12, 24,  4, 27, ...
6  |  1, 2, 1, 5, 4, 8, 2, 11, 7, 14, 4, 17, 10, 20,  1, 23, 13, 26, ...
7  |  1, 3, 3, 6, 2, 9, 6, 12, 1, 15, 9, 18,  5, 21, 12, 24,  4, 27, ...
8  |  1, 2, 1, 5, 4, 8, 2, 11, 7, 14, 4, 17, 10, 20,  1, 23, 13, 26, ...
...
		

Crossrefs

Cf. A257852, A371092, A371100.

Programs

PARI

up_to = 105;
A000265(n) = (n>>valuation(n,2));
A371092(n) = floor((A000265(1+(3*n))+5)/6);
A371100sq(n,k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3;
A371101sq(n,k) = A371092(A371100sq(n,k));
A371101list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A371101sq((a-(col-1)),col))); (v); };
v371101 = A371101list(up_to);
A371101(n) = v371101[n];

Formula

A(n, k) = A371092(A371100(n, k)).

A(n, k) = A(n+2, k).