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Search: id:A054841
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| A054841 |
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If n = 2^a * 3^b * 5^c * 7^d * ... then a(n) = a + 10 * b + 100 * c + 1000 * d + ... |
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+0
11
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| 0, 1, 10, 2, 100, 11, 1000, 3, 20, 101, 10000, 12, 100000, 1001, 110, 4, 1000000, 21, 10000000, 102, 1010, 10001, 100000000, 13, 200, 100001, 30, 1002, 1000000000, 111, 10000000000, 5, 10010, 1000001, 1100, 22, 100000000000, 10000001, 100010
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Are there any other numbers besides n=12 for which n=a(n) ? [From Ctibor O. Zizka (c.zizka(AT)email.cz), Oct 08 2008]
The sequence is a morphism from (N*,*) into (N,+), cf. formula. Up to n=1023, the digit sum A007953(a(n)) equals Omega(n) = A001222(n). This holds whenever A051903(n)<10. Restricted to these n, the sequence is also injective. However, when n is a multiple of 2^10, 3^10, 5^10 etc, then a(n) is equal to some a(m) with m<n. [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 16 2008]
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LINKS
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Evans A Criswell, A Sequence Puzzle (Posted to rec.puzzles Jan 01 1997)
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FORMULA
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a(m*n) = a(m) + a(n) for all m,n > 0. A007953(a(n))=A001222(n) for all n such that A051903(n)<10. [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 16 2008]
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EXAMPLE
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a(25)=200 because 25 = 5^2 * 3^0 * 2^0
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PROGRAM
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(PARI) A054841(n)=sum(i=1, #n=factor(n)~, 10^primepi(n[1, i])*n[2, i])/10 [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 16 2008]
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CROSSREFS
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Cf. A054842, A001222, A048675, A090880, A090881, A090882, A090883, A090884.
Sequence in context: A094715 A096043 A001202 this_sequence A038304 A159005 A144859
Adjacent sequences: A054838 A054839 A054840 this_sequence A054842 A054843 A054844
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KEYWORD
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base,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 11 2000
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