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Search: id:A082276
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| A082276 |
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Smallest number whose digits can be permuted to get exactly n distinct palindromes. |
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+0
1
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| 1, 101, 1001, 10001, 100001, 112233, 10000001, 100122, 10000111
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OFFSET
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1,2
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COMMENT
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Note that 10^n + 1 is always an upper bound.
a(12) = 1000122, a(18) = 10000122, a(30) = 10012233; probably a(24) = 11223344. Any number C(i+j,j) is the number of palindromes from 2i 1's and 2j 2's, so in particular a(10) <= 1111112222 and a(15) <= 111111112222. If a number in this sequence has an odd number of digits, the odd digit must be 0 or 1, with all other digits in pairs; if the number of digits is even, all must be in pairs. The counts of the nonzero digits must be monotonically decreasing (i.e., at least as many 1's as 2's, etc.) - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 26 2006
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EXAMPLE
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101 gives two palindromes 101 and 011 = 11 hence a(2) = 101.
a(6) = 112233, The digit permutation gives six palindromes 123321,132231,213312,231132,312213,321123.
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CROSSREFS
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Cf. A082274, A082275.
Adjacent sequences: A082273 A082274 A082275 this_sequence A082277 A082278 A082279
Sequence in context: A131697 A031423 A089291 this_sequence A069597 A037053 A139535
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KEYWORD
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base,more,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 13 2003
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EXTENSIONS
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More terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 26 2006
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