A255880 a(n) = n-th Rhonda number to base b = n-th composite number, cf. A002808.

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

Author

Reinhard Zumkeller, Mar 10 2015

Keywords

• nonn

Comments

See A099542 for definition of Rhonda numbers and for more links.

Examples

			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]
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, Rhonda Number

Crossrefs

Cf. A002808, A255872, A100968, A100969, A100970, A100973, A099542, A100971, A100972, A100974.

Main diagonal of A291925.

Programs

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

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 *)