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Search: id:A071267
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| A071267 |
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Numbers which can be expressed as the sum of all distinct digit permutations of some number k. |
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+0
1
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 111, 121, 132, 143, 154, 165, 176, 187, 222, 333, 444, 555, 666, 777, 888, 999, 1110, 1111, 1221, 1332, 1443, 1554, 1665, 1776, 1887, 1998, 2109, 2220, 2222, 2331, 2442, 2553, 2664, 2775, 2886
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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222 can be expressed so in two different ways i.e. 222 = 200 + 020 + 002 as well as 222 = 101 + 110 + 011. Question: find a number which can be so expressed in n different ways.
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LINKS
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David W. Wilson, Table of n, a(n) for n = 1..9450
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FORMULA
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Comments from David W. Wilson (davidwwilson(AT)comcast.net), Jul 12 2007 (Start):
Let f(n) be the sum of all permuted versions of n. Let
s(n) = sum of digits of n.
d(n) = number of digits of n.
c_n(k) = number of occurrences of digit k in n.
p(n) = PROD(k = 0..9; c_n(k)!).
r(n) = n-digit rep-1 number = (10^n-1)/n.
t(n) = ((s(n)(d(n)-1)!)/p(n)).
Then f(n) = t(n) r(d(n)).
For example, if n = 314159, we get
s(n) = 23
d(n) = 6
c_n = (0, 2, 0, 1, 1, 1, 0, 0, 0, 1)
p(n) = PROD(k = 0..9; c_n(k)!) = 2
r(d(n)) = r(6) = 111111
t(n) = (23*120)/2 = 1380
and
f(314159) = 1380*11111 = 153333180. (End)
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EXAMPLE
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1110 is a member as a sum of all distinct permutations of 104. i.e. 104,140,410,401,014,041.
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CROSSREFS
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Sequence in context: A109872 A030285 A048321 this_sequence A110784 A082937 A160818
Adjacent sequences: A071264 A071265 A071266 this_sequence A071268 A071269 A071270
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 01 2002
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EXTENSIONS
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Corrected and extended by Diana Mecum (diana.mecum(AT)gmail.com), Jul 06 2007
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