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
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, ...
Columns k=1-11,19,42 give:
A100968,
A100969,
A100970,
A100973,
A099542,
A100971,
A100972,
A100974,
A100975,
A255735,
A255732,
A255736,
A255731.
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
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.
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.
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
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}.
Showing 1-3 of 3 results.
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