A372356 Array read by upward antidiagonals: A(n, k) = A372354(1+n,k)-A372354(n,k), n,k >= 1.

4, 8, 3, 16, 8, 6, 32, 16, 12, 3, 64, 32, 24, 5, 3, 128, 64, 48, 9, 7, 3, 256, 128, 96, 21, 13, 5, 5, 512, 256, 192, 44, 25, 13, 12, 3, 1024, 512, 384, 88, 53, 28, 24, 5, 3, 2048, 1024, 768, 176, 108, 56, 48, 8, 9, 2, 4096, 2048, 1536, 352, 216, 112, 96, 21, 20, 7, 8, 8192, 4096, 3072, 704, 432, 224, 192, 44, 40, 13, 16, 3

Offset: 1

Author

Antti Karttunen, Apr 30 2024

Keywords

• nonn
• tabl

Examples

			Array begins:
n\k|    1     2     3    4    5    6     7    8     9   10    11   12   13   14
---+-----------------------------------------------------------------------------
1  |    4,    3,    6,   3,   3,   3,    5,   3,    3,   2,    8,   3,   4,   3,
2  |    8,    8,   12,   5,   7,   5,   12,   5,    9,   7,   16,   4,   6,   5,
3  |   16,   16,   24,   9,  13,  13,   24,   8,   20,  13,   32,  13,  15,  11,
4  |   32,   32,   48,  21,  25,  28,   48,  21,   40,  25,   64,  28,  29,  21,
5  |   64,   64,   96,  44,  53,  56,   96,  44,   80,  53,  128,  56,  57,  40,
6  |  128,  128,  192,  88, 108, 112,  192,  88,  160, 108,  256, 112, 117,  81,
7  |  256,  256,  384, 176, 216, 224,  384, 176,  320, 216,  512, 224, 236, 161,
8  |  512,  512,  768, 352, 432, 448,  768, 352,  640, 432, 1024, 448, 472, 324,
9  | 1024, 1024, 1536, 704, 864, 896, 1536, 704, 1280, 864, 2048, 896, 944, 647,
		

Crossrefs

Columnwise first differences of A372354.

Cf. A000523, A371094, A372282, A372357.

Programs

PARI

up_to = 78;
A000523(n) = logint(n,2);
A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
A372356sq(n,k) = { my(x=A372282sq(n,k)); (A000523(A371094(x))-A000523(x)); };
A372356list(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] = A372356sq((a-(col-1)),col))); (v); };
v372356 = A372356list(up_to);
A372356(n) = v372356[n];