A100969 -id:A100969 - cp's OEIS frontend

A255735 Integers that are Rhonda numbers to base 18.

1470, 3000, 8918, 17025, 19402, 20650, 21120, 22156, 26522, 36549, 38354, 43281, 46035, 48768, 54229, 54528, 56584, 58216, 58224, 62238, 68096, 68150, 73161, 74024, 74636, 87978, 94041, 114000, 124656, 132240, 133926, 135876, 153105, 153870, 156621, 159819

Offset: 1

Reinhard Zumkeller, Mar 05 2015

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

			a(1) = 1470 = 4*18^2 + 9*18^1 + 12*18^0 = 2*3*5*7*7,
with 4 * 9 * 12 = 18 * (2+3+5+7+7) = 432;
a(10) = 36549 = 6*18^3 + 4*18^2 + 14*18^1 + 9*18^0 = 3*3*31*131,
with 6 * 4 * 14 * 9 = 18 * (3+3+31+131) = 3024.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Rhonda Number

Cf. Rhonda numbers to other bases: A100968 (base 4), A100969 (base 6), A100970 (base 8), A100973 (base 9), A099542 (base 10), A100971 (base 12), A100972 (base 14), A100974 (base 15), A100975 (base 16), A255732 (base 20), A255736 (base 30), A255731 (base 60), A255872.
Cf. A001414, A027746.
Column k=10 of A291925.

a255735 n = a255735_list !! (n-1)
a255735_list = filter (rhonda 18) $ iterate z 1 where
   z x = 1 + if r < 17 then x else 18 * z x' where (x', r) = divMod x 18
-- Function rhonda as in A099542.

A255736 Integers that are Rhonda numbers to base 30.

Original entry on oeis.org

3024, 3168, 5115, 5346, 5950, 6762, 7750, 7956, 8470, 9476, 9576, 9849, 10360, 11495, 13035, 13356, 16335, 22610, 22784, 23864, 37515, 38025, 40704, 40986, 49887, 52925, 59800, 60955, 61812, 67782, 68590, 74800, 78430, 85063, 90160, 90649, 90897, 91540

Offset: 1

Reinhard Zumkeller, Mar 05 2015

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

			a(1) = 3024 = 3 * 30^2 + 10 * 30^1 + 24 * 30^0 = 2*2*2*2*3*3*3*7,
with 3 * 10 * 24 = 30 * (2+2+2+2+3+3+3+7) = 720;
a(10) = 9476 = 10 * 30^2 + 15 * 30^1 + 26 * 30^0 = 2*2*23*103,
with 10 * 15 * 26 = 30 * (2+2+23+103) = 3900.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Rhonda Number

Cf. Rhonda numbers to other bases: A100968 (base 4), A100969 (base 6), A100970 (base 8), A100973 (base 9), A099542 (base 10), A100971 (base 12), A100972 (base 14), A100974 (base 15), A100975 (base 16), A255735 (base 18), A255732 (base 20), A255731 (base 60), see also A255872.
Cf. A001414, A027746.
Column k=19 of A291925.

a255736 n = a255736_list !! (n-1)
a255736_list = filter (rhonda 30) $ iterate z 1 where
   z x = 1 + if r < 29 then x else 30 * z x' where (x', r) = divMod x 30
-- Function rhonda as in A099542.

A255731 Rhonda numbers in sexagesimal number system.

Original entry on oeis.org

3348, 3510, 6750, 17430, 18750, 18876, 18944, 19475, 20564, 21312, 26550, 28280, 37230, 38396, 43940, 48042, 77770, 88270, 91224, 97470, 108882, 111403, 120046, 123630, 181996, 182646, 235467, 253460, 260429, 264735, 278675, 289161, 295960, 296055, 306642

Offset: 1

Reinhard Zumkeller, Mar 05 2015

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

			a(1) = 3348 = 55 * 60^1 + 48 * 60^0 = 2*2*3*3*3*31,
with 55 * 48 = 60 * (2+2+3+3+3+31) = 2640;
a(10) = 21312 = 5*60^2 + 55*60^1 + 12*60^0 = 2*2*2*2*2*2*3*3*37,
with 5 * 55 * 12 = 60 * (2+2+2+2+2+2+3+3+37) = 3300.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Rhonda Number
Wikipedia, Sexagesimal

Cf. Rhonda numbers to other bases: A100968 (base 4), A100969 (base 6), A100970 (base 8), A100973 (base 9), A099542 (base 10), A100971 (base 12), A100972 (base 14), A100974 (base 15), A100975 (base 16), A255735 (base 18), A255732 (base 20), A255736 (base 30).
Cf. A001414, A027746.
Column k=42 of A291925.

a255731 n = a255731_list !! (n-1)
a255731_list = filter (rhonda 60) $ iterate z 1 where
   z x = 1 + if r < 59 then x else 60 * z x' where (x', r) = divMod x 60
-- Function rhonda as in A099542.

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

Original entry on oeis.org

10206, 855, 1836, 15540, 1568, 560, 11475, 2392, 1000, 1470, 1815, 1632, 2695, 2080, 6764, 7788, 4797, 3094, 3024, 1944, 756, 5661, 8232, 1000, 12296, 5824, 4624, 4851, 8262, 6561, 16583, 14616, 6545, 7225, 11310, 18382, 1995, 16896, 2940, 23465, 8464, 3348

Offset: 1

Reinhard Zumkeller, Mar 08 2015

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

			.   n |  b |  a(n)              |  a(n) in base b | factorization
. ----+----+--------------------+-----------------+--------------
.   1 |  4 | 10206 = A100968(1) | [2,1,3,3,1,3,2] | 2*3^6*7
.   2 |  6 |   855 = A100969(1) |       [3,5,4,3] | 3^2*5*19
.   3 |  8 |  1836 = A100970(1) |       [3,4,5,4] | 2^2*3^3*17
.   4 |  9 | 15540 = A100973(1) |     [2,3,2,7,6] | 2^2*3*5*7*37
.   5 | 10 |  1568 = A099542(1) |       [1,5,6,8] | 2^5*7^2
.   6 | 12 |   560 = A100971(1) |        [3,10,8] | 2^4*5*7
.   7 | 14 | 11475 = A100972(1) |       [4,2,7,9] | 3^3*5^2*17
.   8 | 15 |  2392 = A100974(1) |        [10,9,7] | 2^3*13*23
.   9 | 16 |  1000 = A100975(1) |        [3,14,8] | 2^3*5^3
.  10 | 18 |  1470 = A255735(1) |        [4,9,12] | 2*3*5*7^2
.  11 | 20 |  1815 = A255732(1) |       [4,10,15] | 3*5*11^2
.  12 | 21 |  1632              |       [3,14,15] | 2^5*3*17
.  13 | 22 |  2695              |       [5,12,11] | 5*7^2*11
.  14 | 24 |  2080              |       [3,14,16] | 2^5*5*13
.  15 | 25 |  6764              |      [10,20,14] | 2^2*19*89
.  16 | 26 |  7788              |      [11,13,14] | 2^2*3*11*59
.  17 | 27 |  4797              |       [6,15,18] | 3^2*13*41
.  18 | 28 |  3094              |       [3,26,14] | 2*7*13*17
.  19 | 30 |  3024 = A255736(1) |       [3,10,24] | 2^4*3^3*7
.  20 | 32 |  1944              |       [1,28,24] | 2^3*3^5

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Rhonda Number

Cf. A002808, A100968, A100969, A100970, A100973, A099542, A100971, A100972, A100974, A100975, A255735, A255732, A255736.
Cf. A255880.
Row n=1 of A291925.

a255872 n = head $ filter (rhonda b) $ iterate zeroless 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

A248910 Numbers with no zeros in base-6 representation.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92

Offset: 1

Reinhard Zumkeller, Mar 08 2015

Different from A039215, A047253, A184522, A187390, A194386.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Wikipedia, Senary
Index entries for 6-automatic sequences.

Cf. A007092, A100969 (subsequence).

Zeroless numbers in some other bases <= 10: A000042 (base 2), A032924 (base 3), A023705 (base 4), A255805 (base 8), A255808 (base 9), A052382 (base 10).

a248910 n = a248910_list !! (n-1)
a248910_list = iterate f 1 where
   f x = 1 + if r < 5 then x else 6 * f x'  where (x', r) = divMod x 6

Select[Range[100], DigitCount[#,6, 0] == 0 &] (* Paolo Xausa, Jun 29 2025 *)

isok(m) = vecmin(digits(m, 6)) > 0; \\ Michel Marcus, Jan 23 2022

from sympy import integer_log
def A248910(n):
    m = integer_log(k:=(n<<2)+1,5)[0]
    return sum((1+(k-5**m)//(5**j<<2)%5)*6**j for j in range(m)) # Chai Wah Wu, Jun 28 2025

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

Original entry on oeis.org

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

Reinhard Zumkeller, Mar 10 2015

nonn

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

			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]

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

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

Main diagonal of A291925.

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

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 *)

cp's OEIS Frontend

A255735 Integers that are Rhonda numbers to base 18.

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A255736 Integers that are Rhonda numbers to base 30.

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A255731 Rhonda numbers in sexagesimal number system.

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

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A248910 Numbers with no zeros in base-6 representation.

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

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