A372354 Array read by upward antidiagonals: A(n, k) = A000523(A372282(n, k)), n,k >= 1, where A000523(x) is one less than the number of bits in the binary expansion of x.

0, 4, 1, 12, 4, 2, 28, 12, 8, 2, 60, 28, 20, 5, 3, 124, 60, 44, 10, 6, 3, 252, 124, 92, 19, 13, 6, 3, 508, 252, 188, 40, 26, 11, 8, 3, 1020, 508, 380, 84, 51, 24, 20, 6, 4, 2044, 1020, 764, 172, 104, 52, 44, 11, 7, 4, 4092, 2044, 1532, 348, 212, 108, 92, 19, 16, 6, 4, 8188, 4092, 3068, 700, 428, 220, 188, 40, 36, 13, 12, 4

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Example

Array begins:
n\k|    1     2     3    4    5    6     7    8     9   10    11   12   13   14
---+-----------------------------------------------------------------------------
1  |    0,    1,    2,   2,   3,   3,    3,   3,    4,   4,    4,   4,   4,   4,
2  |    4,    4,    8,   5,   6,   6,    8,   6,    7,   6,   12,   7,   8,   7,
3  |   12,   12,   20,  10,  13,  11,   20,  11,   16,  13,   28,  11,  14,  12,
4  |   28,   28,   44,  19,  26,  24,   44,  19,   36,  26,   60,  24,  29,  23,
5  |   60,   60,   92,  40,  51,  52,   92,  40,   76,  51,  124,  52,  58,  44,
6  |  124,  124,  188,  84, 104, 108,  188,  84,  156, 104,  252, 108, 115,  84,
7  |  252,  252,  380, 172, 212, 220,  380, 172,  316, 212,  508, 220, 232, 165,
8  |  508,  508,  764, 348, 428, 444,  764, 348,  636, 428, 1020, 444, 468, 326,
9  | 1020, 1020, 1532, 700, 860, 892, 1532, 700, 1276, 860, 2044, 892, 940, 650,

Prog

(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)));
A372354sq(n, k) = A000523(A372282sq(n, k));
A372354list(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] = A372354sq((a-(col-1)), col))); (v); };
v372354 = A372354list(up_to);
A372354(n) = v372354[n];

Crossrefs

Cf. A000523, A371094, A372282, A372356 (columnwise first differences), A372357.

Row 1 is 0 followed by A113473.

Sequence in context: A145370 A130322 A316232 * A366885 A212046 A232013

Adjacent sequences: A372351 A372352 A372353 * A372355 A372356 A372357

Keyword

nonn,tabl,easy

Author

Antti Karttunen, Apr 30 2024

Status

approved