A372355 Array read by upward antidiagonals: A(n,k) = A372285(1+n, k)-A372285(n, k), n,k >= 1.

4, 8, 5, 16, 8, 6, 32, 16, 12, 3, 64, 32, 24, 5, 2, 128, 64, 48, 12, 7, 3, 256, 128, 96, 23, 13, 8, 7, 512, 256, 192, 44, 28, 15, 12, 1, 1024, 512, 384, 88, 55, 28, 24, 5, 6, 2048, 1024, 768, 176, 108, 56, 48, 13, 11, 3, 4096, 2048, 1536, 352, 216, 112, 96, 23, 20, 7, 8, 8192, 4096, 3072, 704, 432, 224, 192, 44, 40, 13, 16, 3

Offset

1,1

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
---+----------------------------------------------------------------------------
1  |    4,    5,     6,    3,    2,    3,     7,    1,     6,    3,     8,    3,
2  |    8,    8,    12,    5,    7,    8,    12,    5,    11,    7,    16,    9,
3  |   16,   16,    24,   12,   13,   15,    24,   13,    20,   13,    32,   15,
4  |   32,   32,    48,   23,   28,   28,    48,   23,    40,   28,    64,   28,
5  |   64,   64,    96,   44,   55,   56,    96,   44,    80,   55,   128,   56,
6  |  128,  128,   192,   88,  108,  112,   192,   88,   160,  108,   256,  112,
7  |  256,  256,   384,  176,  216,  224,   384,  176,   320,  216,   512,  224,
8  |  512,  512,   768,  352,  432,  448,   768,  352,   640,  432,  1024,  448,
9  | 1024, 1024,  1536,  704,  864,  896,  1536,  704,  1280,  864,  2048,  896,
10 | 2048, 2048,  3072, 1408, 1728, 1792,  3072, 1408,  2560, 1728,  4096, 1792,
11 | 4096, 4096,  6144, 2816, 3456, 3584,  6144, 2816,  5120, 3456,  8192, 3584,
12 | 8192, 8192, 12288, 5632, 6912, 7168, 12288, 5632, 10240, 6912, 16384, 7168,

Prog

(PARI)
up_to = 78;
A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3); \\ From A086893
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)));
A372286(n) = { my(u=A371094(n), k1); for(i=1, oo, if(A086893(i)>=n, k1=i-1; break)); for(i=k1, oo, if(A086893(i)>u, return(i-k1-1))); };
A372355sq(n, k) = (A372286(A372282sq(1+n, k))-A372286(A372282sq(n, k)));
A372355list(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] = A372355sq((a-(col-1)), col))); (v); };
v372355 = A372355list(up_to);
A372355(n) = v372355[n];

Crossrefs

Columnwise first differences of A372285.

Cf. A086893, A372282, A372286.

Cf. also A372353.

Sequence in context: A276577 A011366 A363873 * A005133 A198241 A175475

Adjacent sequences: A372352 A372353 A372354 * A372356 A372357 A372358

Keyword

nonn,tabl

Author

Antti Karttunen, Apr 29 2024

Status

approved