A291925 - OEIS

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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

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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