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

%I A255880 #16 Feb 16 2025 08:33:25
%S A255880 10206,1029,6622,44360,5439,4888,58404,20079,26296,36549,52059,61376,
%T A255880 131427,29106,165504,137007,63525,61115,22784,135705,658896,563159,
%U A255880 208369,115506,1078784,228436,152308,185571,539213,152532,2289001,193963,2499742,298768
%N A255880 a(n) = n-th Rhonda number to base b = n-th composite number, cf. A002808.
%C A255880 See A099542 for definition of Rhonda numbers and for more links.
%H A255880 Reinhard Zumkeller, <a href="/A255880/b255880.txt">Table of n, a(n) for n = 1..100</a>
%H A255880 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RhondaNumber.html">Rhonda Number</a>
%e A255880 Diagonalization of Rhonda numbers to base b = A002808(n), n = 1 .. 8:
%e A255880 .   b | n\n              1      2     3      4      5     6      7      8
%e A255880 . ----+---+---------------------------------------------------------------
%e A255880 .   4 | 1 | A100968 [10206] 11935 12150  16031  45030 94185 113022 114415
%e A255880 .   6 | 2 | A100969    855  [1029] 3813   5577   7040  7304  15104  19136
%e A255880 .   8 | 3 | A100970   1836   6318 [6622] 10530  14500 14739  17655  18550
%e A255880 .   9 | 4 | A100973  15540  21054 25331 [44360] 44660 44733  47652  50560
%e A255880 .  10 | 5 | A099542   1568   2835  4752   5265  [5439] 5664   5824   5832
%e A255880 .  12 | 6 | A100971    560    800  3993   4425   4602 [4888]  7315   8296
%e A255880 .  14 | 7 | A100972  11475  18655 20565  29631  31725 45387 [58404] 58667
%e A255880 .  15 | 8 | A100974   2392   2472 11468  15873  17424 18126  19152 [20079]
%t A255880 nc = 34; (* number of composite bases *)
%t A255880 compos = Select[Range[FindRoot[n == nc + PrimePi[n] + 1, {n, nc, 2nc}][[1, 2]] // Floor], CompositeQ];
%t A255880 RhondaQ[n_, b_] := Times @@ IntegerDigits[n, b] == b Total[Times @@@ FactorInteger[n]];
%t A255880 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]]]]];
%t A255880 Table[Print[n, " ", a[n]]; a[n], {n, 1, nc}] (* _Jean-François Alcover_, Nov 15 2021 *)
%o A255880 (Haskell)
%o A255880 a255880 n = (filter (rhonda b) $ iterate zeroless 1) !! (n - 1) where
%o A255880             -- function rhonda as defined in A099542
%o A255880             zeroless x = 1 + if r < b - 1 then x else b * zeroless x'
%o A255880                          where (x', r) = divMod x b
%o A255880             b = a002808 n
%Y A255880 Cf. A002808, A255872, A100968, A100969, A100970, A100973, A099542, A100971, A100972, A100974.
%Y A255880 Main diagonal of A291925.
%K A255880 nonn
%O A255880 1,1
%A A255880 _Reinhard Zumkeller_, Mar 10 2015