A100971 Integers that are Rhonda numbers to base 12.

560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264, 18511, 18906, 25619, 25875, 27176, 32742, 37264, 37523, 46035, 50765, 52338, 58261, 58504, 59166, 62002, 66176, 66752, 66928, 67195, 68502

Offset

1,1

Comments

See sequence A099542 for the definition of Rhonda numbers and some links. 560 is the smallest integer that is a Rhonda number to some base.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Kevin S. Brown's Mathpages, Infinitely Many Rhondas.

Eric Weisstein's World of Mathematics, Rhonda Number.

Wikipedia, Duodecimal.

Example

The product of the base 12 digits of 560 is 3*10*8=240; the sum of the prime factors of 560 is 4*2+5+7=20; and 240=12*20 so 560 is a Rhonda number to base 12.

Mathematica

With[{b = 12}, Select[Range[b^5], Times @@ IntegerDigits[#, b] == b*Total[Times @@@ FactorInteger[#]] &] ] (* Michael De Vlieger, Jan 23 2026 *)

Prog

(Haskell)
a100971 n = a100971_list !! (n-1)
a100971_list = filter (rhonda 12) $ iterate z 1 where
   z x = 1 + if r < 11 then x else 12 * z x' where (x', r) = divMod x 12
-- Function rhonda as in A099542.
-- Reinhard Zumkeller, Mar 07 2015

Crossrefs

Cf. Rhonda numbers to other bases: A100968 (base 4), A100969 (base 6), A100970 (base 8), A100973 (base 9), A099542 (base 10), A100972 (base 14), A100974 (base 15), A100975 (base 16), A255735 (base 18), A255732 (base 20), A255736 (base 30), A255731 (base 60).

Cf. A001414, A027746, A255872.

Column k=6 of A291925.

Sequence in context: A136346 A234263 A100987 * A253362 A217986 A260290

Adjacent sequences: A100968 A100969 A100970 * A100972 A100973 A100974

Keyword

easy,nonn,base

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 25 2004

Status

approved