A100975 -id:A100975 - 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

A100987 Integers that are Rhonda numbers to some base.

Original entry on oeis.org

560, 756, 800, 855, 1000, 1029, 1134, 1470, 1568, 1632, 1750, 1815, 1836, 1944, 1995, 2080, 2100, 2392, 2472, 2662, 2695, 2709, 2835, 2940, 3000, 3024, 3060, 3087, 3094, 3168, 3240, 3264, 3348, 3456, 3510, 3600, 3672, 3675, 3744, 3750, 3813, 3888, 3952, 3976

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 25 2004

See sequence A099542 for definition of Rhonda numbers and for some links.

			560 is a Rhonda number to base 12. 756 is a Rhonda number to base 33. 800 is a Rhonda number to base 12 etc. No integer smaller than 560 is a Rhonda number and there exists no Rhonda number between 560 and 756.

Eric Weisstein's World of Mathematics, Rhonda Number

Cf. A099542 for definition of Rhonda numbers. A100968-A100975 for Rhonda numbers for specific bases.

Cf. A291925.

Offset changed to 1 by Alois P. Heinz, Sep 09 2017

A100988 Integers that are Rhonda numbers to more than one base.

Original entry on oeis.org

1000, 2940, 4200, 4212, 4725, 5670, 5824, 5832, 6776, 6864, 7040, 7140, 8296, 9476, 9633, 10200, 11016, 11050, 11160, 11495, 11935, 12393, 12474, 13068, 13260, 13671, 14014, 14322, 14406, 15680, 15750, 15912, 16240, 16821, 17056, 17820, 18270, 18655, 18700

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 25 2004

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

			1000 is a Rhonda number to bases 16 and 36. 2940 is a Rhonda number to bases 56 and 76. 5670 is a Rhonda number to bases 36, 106, 108 and 196.

Eric Weisstein's World of Mathematics, Rhonda Number

Cf. A099542 for definition of Rhonda numbers. A100968 to A100975 for Rhonda numbers to specific bases. A100987 for integers that are Rhonda numbers to some base.

Cf. A291925.

New offset and terms a(12)-a(39) from Alois P. Heinz, Sep 09 2017

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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A100987 Integers that are Rhonda numbers to some base.

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A100988 Integers that are Rhonda numbers to more than one base.

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