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Search: id:A110454
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| A110454 |
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Largest composite number obtained by concatenation of parts of a distinct partition of n, or 0 if no such number exist. |
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+0
1
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| 0, 0, 21, 0, 32, 321, 412, 512, 621, 4321, 5321, 6321, 7312, 8321, 54321, 64321, 74321, 84321, 94312, 432110, 654321, 754321, 854321, 954321, 5432110, 6432110, 7432110, 8432110, 9432110, 9654321, 65432110, 75432110, 85432110, 95432110, 96432110
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Conjecture a(n) = 0 only for n = 1,2 and 4.
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EXAMPLE
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The partitions of 9 are 9, (8, 1), (7, 2), (6, 3), ...(6, 2, 1), (5, 3, 1), (4, 3, 2) etc. (432 is the largest number obtained as a concatenation of 4, 3, 2).
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MAPLE
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catL := proc(L) local a, i ; a := op(-1, L) ; for i from 2 to nops(L) do a := a*10^(max(1, ilog10(op(-i, L))+1))+op(-i, L) ; od: RETURN(a) ; end: A110454 := proc(n) local a, p, m, j ; a := 0 ; for p in combinat[partition](n) do if nops(p) = nops( convert(p, set)) then for j in combinat[permute](p) do m := catL(j) ; if ( m > 4 and not isprime(m) ) and ( m > a) then a := m ; fi ; od: fi ; od: RETURN(a) ; end: for n from 1 do printf("%d, ", A110454(n)) ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2008
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CROSSREFS
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Sequence in context: A128671 A048948 A167263 this_sequence A013547 A040445 A040446
Adjacent sequences: A110451 A110452 A110453 this_sequence A110455 A110456 A110457
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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), Aug 04 2005
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EXTENSIONS
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a(9) corrected by James Sellers, Nov 18 2005
Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2008
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