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A100971 Integers that are Rhonda numbers to base 12.

%I A100971 #14 Jul 01 2025 10:35:32
%S A100971 560,800,3993,4425,4602,4888,7315,8296,9315,11849,12028,13034,14828,
%T A100971 15052,16264,18511,18906,25619,25875,27176,32742,37264,37523,46035,
%U A100971 50765,52338,58261,58504,59166,62002,66176,66752,66928,67195,68502
%N A100971 Integers that are Rhonda numbers to base 12.
%C A100971 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.
%H A100971 Reinhard Zumkeller, <a href="/A100971/b100971.txt">Table of n, a(n) for n = 1..1000</a>
%H A100971 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RhondaNumber.html">Rhonda Number</a>
%H A100971 Wikipedia, <a href="http://www.wikipedia.org/wiki/Duodecimal">Duodecimal</a>
%e A100971 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.
%o A100971 (Haskell)
%o A100971 a100971 n = a100971_list !! (n-1)
%o A100971 a100971_list = filter (rhonda 12) $ iterate z 1 where
%o A100971    z x = 1 + if r < 11 then x else 12 * z x' where (x', r) = divMod x 12
%o A100971 -- Function rhonda as in A099542.
%o A100971 -- _Reinhard Zumkeller_, Mar 07 2015
%Y A100971 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).
%Y A100971 Cf. A001414, A027746, A255872.
%Y A100971 Column k=6 of A291925.
%K A100971 easy,nonn,base
%O A100971 1,1
%A A100971 Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 25 2004