A291925 A(n,k) is the n-th Rhonda number to base A002808(k), the k-th composite number; square array A(n,k), n>=1, k>=1, read by antidiagonals.

10206, 855, 11935, 1836, 1029, 12150, 15540, 6318, 3813, 16031, 1568, 21054, 6622, 5577, 45030, 560, 2835, 25331, 10530, 7040, 94185, 11475, 800, 4752, 44360, 14500, 7304, 113022, 2392, 18655, 3993, 5265, 44660, 14739, 15104, 114415, 1000, 2472, 20565, 4425, 5439, 44733, 17655, 19136, 191149

Offset: 1

Author

Alois P. Heinz, Sep 05 2017

Keywords

• nonn
• tabl
• look

Comments

Integer m is Rhonda number to base b if the product of its base-b digits divided by b is equal to the integer log of m, A001414(m). This can only happen if b is a composite number, b in {A002808}.

Examples

			A(1,2) = 855 is the first and smallest term of column k=2. The second composite number is A002808(2) = 6.  855 = (((3*6)+5)*6+4)*6+3 = 3543_6 = 3*3*5*19. And (3*5*4*3)/6 = A001414(855) = 3+3+5+19 = 30.
Square array A(n,k) begins:
:  10206,   855,  1836, 15540, 1568,  560, 11475, ...
:  11935,  1029,  6318, 21054, 2835,  800, 18655, ...
:  12150,  3813,  6622, 25331, 4752, 3993, 20565, ...
:  16031,  5577, 10530, 44360, 5265, 4425, 29631, ...
:  45030,  7040, 14500, 44660, 5439, 4602, 31725, ...
:  94185,  7304, 14739, 44733, 5664, 4888, 45387, ...
: 113022, 15104, 17655, 47652, 5824, 7315, 58404, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 1..141, flattened
• Eric Weisstein's World of Mathematics, Rhonda Number

Crossrefs

Columns k=1-11,19,42 give: A100968, A100969, A100970, A100973, A099542, A100971, A100972, A100974, A100975, A255735, A255732, A255736, A255731.

Row n=1 gives A255872.

Main diagonal gives A255880.

Cf. A001414, A002808, A100987, A100988, A217986.