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A255880
a(n) = n-th Rhonda number to base b = n-th composite number, cf. A002808.
4
10206, 1029, 6622, 44360, 5439, 4888, 58404, 20079, 26296, 36549, 52059, 61376, 131427, 29106, 165504, 137007, 63525, 61115, 22784, 135705, 658896, 563159, 208369, 115506, 1078784, 228436, 152308, 185571, 539213, 152532, 2289001, 193963, 2499742, 298768
OFFSET
1,1
COMMENTS
See A099542 for definition of Rhonda numbers and for more links.
LINKS
Eric Weisstein's World of Mathematics, Rhonda Number
EXAMPLE
Diagonalization of Rhonda numbers to base b = A002808(n), n = 1 .. 8:
. b | n\n 1 2 3 4 5 6 7 8
. ----+---+---------------------------------------------------------------
. 4 | 1 | A100968 [10206] 11935 12150 16031 45030 94185 113022 114415
. 6 | 2 | A100969 855 [1029] 3813 5577 7040 7304 15104 19136
. 8 | 3 | A100970 1836 6318 [6622] 10530 14500 14739 17655 18550
. 9 | 4 | A100973 15540 21054 25331 [44360] 44660 44733 47652 50560
. 10 | 5 | A099542 1568 2835 4752 5265 [5439] 5664 5824 5832
. 12 | 6 | A100971 560 800 3993 4425 4602 [4888] 7315 8296
. 14 | 7 | A100972 11475 18655 20565 29631 31725 45387 [58404] 58667
. 15 | 8 | A100974 2392 2472 11468 15873 17424 18126 19152 [20079]
MATHEMATICA
nc = 34; (* number of composite bases *)
compos = Select[Range[FindRoot[n == nc + PrimePi[n] + 1, {n, nc, 2nc}][[1, 2]] // Floor], CompositeQ];
RhondaQ[n_, b_] := Times @@ IntegerDigits[n, b] == b Total[Times @@@ FactorInteger[n]];
a[n_] := a[n] = Module[{b = compos[[n]], cnt = 0, k}, For[k = 1, True, k++, If[RhondaQ[k, b], cnt++; If[cnt == n, Return[k]]]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, nc}] (* Jean-François Alcover, Nov 15 2021 *)
PROG
(Haskell)
a255880 n = (filter (rhonda b) $ iterate zeroless 1) !! (n - 1) where
-- function rhonda as defined in A099542
zeroless x = 1 + if r < b - 1 then x else b * zeroless x'
where (x', r) = divMod x b
b = a002808 n
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 10 2015
STATUS
approved