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A255872 Smallest Rhonda number to base b = n-th composite number, A002808(n).

%I A255872 #17 Jul 01 2025 10:42:37
%S A255872 10206,855,1836,15540,1568,560,11475,2392,1000,1470,1815,1632,2695,
%T A255872 2080,6764,7788,4797,3094,3024,1944,756,5661,8232,1000,12296,5824,
%U A255872 4624,4851,8262,6561,16583,14616,6545,7225,11310,18382,1995,16896,2940,23465,8464,3348
%N A255872 Smallest Rhonda number to base b = n-th composite number, A002808(n).
%C A255872 See A099542 for definition of Rhonda numbers and for more links.
%H A255872 Reinhard Zumkeller, <a href="/A255872/b255872.txt">Table of n, a(n) for n = 1..1000</a>
%H A255872 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RhondaNumber.html">Rhonda Number</a>
%e A255872 .   n |  b |  a(n)              |  a(n) in base b | factorization
%e A255872 . ----+----+--------------------+-----------------+--------------
%e A255872 .   1 |  4 | 10206 = A100968(1) | [2,1,3,3,1,3,2] | 2*3^6*7
%e A255872 .   2 |  6 |   855 = A100969(1) |       [3,5,4,3] | 3^2*5*19
%e A255872 .   3 |  8 |  1836 = A100970(1) |       [3,4,5,4] | 2^2*3^3*17
%e A255872 .   4 |  9 | 15540 = A100973(1) |     [2,3,2,7,6] | 2^2*3*5*7*37
%e A255872 .   5 | 10 |  1568 = A099542(1) |       [1,5,6,8] | 2^5*7^2
%e A255872 .   6 | 12 |   560 = A100971(1) |        [3,10,8] | 2^4*5*7
%e A255872 .   7 | 14 | 11475 = A100972(1) |       [4,2,7,9] | 3^3*5^2*17
%e A255872 .   8 | 15 |  2392 = A100974(1) |        [10,9,7] | 2^3*13*23
%e A255872 .   9 | 16 |  1000 = A100975(1) |        [3,14,8] | 2^3*5^3
%e A255872 .  10 | 18 |  1470 = A255735(1) |        [4,9,12] | 2*3*5*7^2
%e A255872 .  11 | 20 |  1815 = A255732(1) |       [4,10,15] | 3*5*11^2
%e A255872 .  12 | 21 |  1632              |       [3,14,15] | 2^5*3*17
%e A255872 .  13 | 22 |  2695              |       [5,12,11] | 5*7^2*11
%e A255872 .  14 | 24 |  2080              |       [3,14,16] | 2^5*5*13
%e A255872 .  15 | 25 |  6764              |      [10,20,14] | 2^2*19*89
%e A255872 .  16 | 26 |  7788              |      [11,13,14] | 2^2*3*11*59
%e A255872 .  17 | 27 |  4797              |       [6,15,18] | 3^2*13*41
%e A255872 .  18 | 28 |  3094              |       [3,26,14] | 2*7*13*17
%e A255872 .  19 | 30 |  3024 = A255736(1) |       [3,10,24] | 2^4*3^3*7
%e A255872 .  20 | 32 |  1944              |       [1,28,24] | 2^3*3^5
%o A255872 (Haskell)
%o A255872 a255872 n = head $ filter (rhonda b) $ iterate zeroless 1 where
%o A255872             -- function rhonda as defined in A099542
%o A255872             zeroless x = 1 + if r < b - 1 then x else b * zeroless x'
%o A255872                          where (x', r) = divMod x b
%o A255872             b = a002808 n
%Y A255872 Cf. A002808, A100968, A100969, A100970, A100973, A099542, A100971, A100972, A100974, A100975, A255735, A255732, A255736.
%Y A255872 Cf. A255880.
%Y A255872 Row n=1 of A291925.
%K A255872 nonn,base
%O A255872 1,1
%A A255872 _Reinhard Zumkeller_, Mar 08 2015