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A110454
Largest composite number obtained by concatenation of parts of a distinct partition of n, or 0 if no such number exist.
1
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
OFFSET
1,3
COMMENTS
Conjecture a(n) = 0 only for n = 1, 2 and 4.
EXAMPLE
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).
MAPLE
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: # R. J. Mathar, Feb 08 2008
CROSSREFS
Sequence in context: A167263 A324685 A224114 * A265156 A040445 A040446
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Aug 04 2005
EXTENSIONS
a(9) corrected by James A. Sellers, Nov 18 2005
Corrected and extended by R. J. Mathar, Feb 08 2008
STATUS
approved