48 lines
2.3 KiB
Text
48 lines
2.3 KiB
Text
A positive integer '''''n''''' is said to be a Rhonda number to base '''''b''''' if the product of the base '''''b''''' digits of '''''n''''' is equal to '''''b''''' times the sum of '''''n''''''s prime factors.
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''These numbers were named by Kevin Brown after an acquaintance of his whose residence number was 25662, a member of the base 10 numbers with this property.''
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'''25662''' is a Rhonda number to base-'''10'''. The prime factorization is '''2 × 3 × 7 × 13 × 47'''; the product of its base-'''10''' digits is equal to the base times the sum of its prime factors:
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<span style=font-size:150%;font-weight:bold;padding-left:3em;>2 × 5 × 6 × 6 × 2 = 720 = 10 × (2 + 3 + 7 + 13 + 47)</span>
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Rhonda numbers only exist in bases that are not a prime.
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''Rhonda numbers to base 10 '''always''' contain at least 1 digit 5 and '''always''' contain at least 1 even digit.''
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;Task
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* For the non-prime bases '''''b''''' from '''2''' through '''16''' , find and display here, on this page, at least the first '''10''' '''Rhonda numbers''' to base '''''b'''''. Display the found numbers at least in base '''10'''.
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;Stretch
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* Extend out to base '''36'''.
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;See also
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;* [https://mathworld.wolfram.com/RhondaNumber.html Wolfram Mathworld - Rhonda numbers]
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;* [https://www.numbersaplenty.com/set/Rhonda_number Numbers Aplenty - Rhonda numbers]
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;* [[oeis:A100968|OEIS:A100968 - Integers n that are Rhonda numbers to base 4]]
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;* [[oeis:A100969|OEIS:A100969 - Integers n that are Rhonda numbers to base 6]]
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;* [[oeis:A100970|OEIS:A100970 - Integers n that are Rhonda numbers to base 8]]
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;* [[oeis:A100973|OEIS:A100973 - Integers n that are Rhonda numbers to base 9]]
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;* [[oeis:A099542|OEIS:A099542 - Rhonda numbers to base 10]]
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;* [[oeis:A100971|OEIS:A100971 - Integers n that are Rhonda numbers to base 12]]
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;* [[oeis:A100972|OEIS:A100972 - Integers n that are Rhonda numbers to base 14]]
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;* [[oeis:A100974|OEIS:A100974 - Integers n that are Rhonda numbers to base 15]]
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;* [[oeis:A100975|OEIS:A100975 - Integers n that are Rhonda numbers to base 16]]
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;* [[oeis:A255735|OEIS:A255735 - Integers n that are Rhonda numbers to base 18]]
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;* [[oeis:A255732|OEIS:A255732 - Rhonda numbers in vigesimal number system]] (base 20)
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;* [[oeis:A255736|OEIS:A255736 - Integers that are Rhonda numbers to base 30]]
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;* [[Smith numbers|Related Task: Smith numbers]]
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<br>
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