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.

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, ...
		

Crossrefs

Row n=1 gives A255872.
Main diagonal gives A255880.

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

Views

Author

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

Keywords

Comments

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

Examples

			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.
		

Crossrefs

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.

Extensions

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

A217986 The smallest k that is a Rhonda number in exactly n bases.

Original entry on oeis.org

560, 1000, 10200, 5670, 63945, 158400, 322920, 140800, 1200420, 889200, 792064, 4706352, 6331446, 12042800, 1000350, 8429960, 101892288, 129600900, 365575680, 340692480, 264269250, 304646400, 511999488, 118857024
Offset: 1

Views

Author

Giovanni Resta, Oct 17 2012

Keywords

Comments

n is a Rhonda number in base B if the product of its digits in base B is equal to B times the sum of its prime factors (with multiplicity).

Examples

			a(3)=10200 since 10200=2^3*3*5^2*17, so sopf=36. Its representations in bases 130,174, and 238 are (78,60)_130, (58,108)_174 and (42, 204)_238.
Finally, we have 78*60=130*36, 58*108=174*36, 42*204=238*36 and no smaller number is a Rhonda number w.r.t. exactly 3 bases.
a(24)=118857024 is a Rhonda number in bases {65412, 73593, 97020, 111176, 138996, 190125, 215644, 239057, 250120, 312576, 329004, 354497, 451308, 465426, 544128, 562104, 640692, 778752, 888888, 930402, 1026168, 1101672, 1165944, 1213082}.
		

Crossrefs

Cf. A099542 (for more links), A100987.
Showing 1-3 of 3 results.