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Search: id:A083970
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| A083970 |
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Numbers n such that concatenation R(n) and n is divisible by n. |
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+0
2
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 25, 30, 33, 36, 40, 44, 45, 48, 50, 55, 60, 66, 70, 75, 77, 80, 88, 90, 99, 100, 101, 110, 111, 120, 121, 125, 131, 132, 141, 150, 151, 161, 165, 168, 171, 180, 181, 191, 198, 200, 202, 212, 220, 222, 225, 232
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All palindromes (in decimal) occur in this sequence. If we can multiply a(k) by j without having to resort to any carrying over, than ja(k) is also in the sequence. - Sam Alexander (amnalexander(AT)yahoo.com), Oct 21 2003
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FORMULA
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Saying that R(n) concat n is divisible by n is equivalent to saying that (10^d)R(n) is divisible by n, where d = the number of digits in n. It follows that for any given n in this sequence, either n is a palindrome or n and 10 are not relatively prime. - Sam Alexander (amnalexander(AT)yahoo.com), Oct 21 2003
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EXAMPLE
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12 is a member as 2112 is divisible by 12 and 13 is not as 3113 is not divisible by 13.
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CROSSREFS
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Cf. A083971.
Sequence in context: A023781 A135578 A050607 this_sequence A071204 A002796 A055471
Adjacent sequences: A083967 A083968 A083969 this_sequence A083971 A083972 A083973
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), May 21 2003
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EXTENSIONS
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Corrected and extended by Sam Alexander (amnalexander(AT)yahoo.com), Oct 21 2003
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