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

1,1

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}.

Links

Alois P. Heinz, Antidiagonals n = 1..141, flattened

Eric Weisstein's World of Mathematics, Rhonda Number

Example

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, ...

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.

Sequence in context: A243819 A258890 A255872 * A255880 A100968 A203056

Adjacent sequences: A291922 A291923 A291924 * A291926 A291927 A291928

Keyword

nonn,tabl,look

Author

Alois P. Heinz, Sep 05 2017

Status

approved