cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A099542 Rhonda numbers to base 10.

Original entry on oeis.org

1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662, 33475, 34935, 35581, 45951, 47265, 47594, 52374, 53176, 53742, 54479, 55272, 56356, 56718, 95232, 118465, 133857, 148653, 154462, 161785
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 21 2004

Keywords

Comments

An integer m is a Rhonda number to base b if the product of its digits in base b equals b*(sum of prime factors of m (taken with multiplicity)).
Does every Rhonda number to base 10 contain at least one 5? - Howard Berman (howard_berman(AT)hotmail.com), Oct 22 2008
Yes, every Rhonda number m to base 10 contains at least one 5 and also one even digit, otherwise A007954(m) mod 10 > 0. - Reinhard Zumkeller, Dec 01 2012

Examples

			1568 has prime factorization 2^5 * 7^2. Sum of prime factors = 2*5 + 7*2 = 24. Product of digits of 1568 = 1*5*6*8 = 240 = 10*24, hence 1568 is a Rhonda number to base 10.

Links

Crossrefs

Cf. Rhonda numbers to other bases: A100968 (base 4), A100969 (base 6), A100970 (base 8), A100973 (base 9), A100971 (base 12), A100972 (base 14), A100974 (base 15), A100975 (base 16), A255735 (base 18), A255732 (base 20), A255736 (base 30), A255731 (base 60), see also A255880.
Cf. A001414, A027746, A007954.
Column k=5 of A291925.

Programs

  • Haskell
    import Data.List (unfoldr); import Data.Tuple (swap)
a099542 n = a099542_list !! (n-1)
a099542_list = filter (rhonda 10) [1..]
rhonda b x = a001414 x * b == product (unfoldr
       (\z -> if z == 0 then Nothing else Just $ swap $ divMod z b) x)
-- Reinhard Zumkeller, Mar 05 2015, Dec 01 2012
  • Mathematica
    Select[Range[200000],10Total[Times@@@FactorInteger[#]]==Times@@ IntegerDigits[ #]&] (* Harvey P. Dale, Oct 16 2011 *)

Formula

A007954(a(n)) = 10 * A001414(a(n)).

A291925 A(n,k) is the n-th Rhonda number to base A002808(k), the k-th composite number; square array A(n,k), n>=1, k>=1, read by antidiagonals.

Original entry on oeis.org

10206, 855, 11935, 1836, 1029, 12150, 15540, 6318, 3813, 16031, 1568, 21054, 6622, 5577, 45030, 560, 2835, 25331, 10530, 7040, 94185, 11475, 800, 4752, 44360, 14500, 7304, 113022, 2392, 18655, 3993, 5265, 44660, 14739, 15104, 114415, 1000, 2472, 20565, 4425, 5439, 44733, 17655, 19136, 191149
Offset: 1

Views

Author

Alois P. Heinz, Sep 05 2017

Keywords

Comments

Integer m is Rhonda number to base b if the product of its base-b digits divided by b is equal to the integer log of m, A001414(m). This can only happen if b is a composite number, b in {A002808}.

Examples

			A(1,2) = 855 is the first and smallest term of column k=2. The second composite number is A002808(2) = 6.  855 = (((3*6)+5)*6+4)*6+3 = 3543_6 = 3*3*5*19. And (3*5*4*3)/6 = A001414(855) = 3+3+5+19 = 30.
Square array A(n,k) begins:
:  10206,   855,  1836, 15540, 1568,  560, 11475, ...
:  11935,  1029,  6318, 21054, 2835,  800, 18655, ...
:  12150,  3813,  6622, 25331, 4752, 3993, 20565, ...
:  16031,  5577, 10530, 44360, 5265, 4425, 29631, ...
:  45030,  7040, 14500, 44660, 5439, 4602, 31725, ...
:  94185,  7304, 14739, 44733, 5664, 4888, 45387, ...
: 113022, 15104, 17655, 47652, 5824, 7315, 58404, ...

Links

Crossrefs

Columns k=1-11,19,42 give: A100968, A100969, A100970, A100973, A099542, A100971, A100972, A100974, A100975, A255735, A255732, A255736, A255731.
Row n=1 gives A255872.
Main diagonal gives A255880.
Cf. A001414, A002808, A100987, A100988, A217986.

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

Views

Author

Reinhard Zumkeller, Mar 08 2015

Keywords

Comments

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

Examples

			.   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

Links

Crossrefs

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

Programs

  • Haskell
    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
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.