A110454 Largest composite number obtained by concatenation of parts of a distinct partition of n, or 0 if no such number exist.

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.

Links

Table of n, a(n) for n=1..35.

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

Adjacent sequences: A110451 A110452 A110453 * A110455 A110456 A110457

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