bibkey: murthy2005a110454
authors: Amarnath Murthy
year: 2005
title: "OEIS A110454, Largest composite number obtained by concatenation of parts of a distinct partition of n"
doi: null
url: https://oeis.org/A110454
claim: "Largest composite number obtained by concatenation of parts of a distinct partition of n, or 0 if no such number exist. Conjecture a(n) = 0 only for n = 1, 2 and 4. - _Amarnath Murthy_, Aug 04 2005"
strata_touched:
  - D5/S1/Digit/Admissibility/DistinctPartitionConcatenationComposite
license: citation-only
triage: anchor

OEIS A110454

Amarnath Murthy’s comment of August 4, 2005 states the zero-index conjecture quoted above. The entry defines a(n) as the largest composite number obtained by concatenating the parts of a distinct partition of n, or zero when no such number exists.

The Maple program ranges over every partition whose parts are pairwise distinct and over every permutation of those parts. It accepts a concatenation m exactly when m > 4 and m is not prime. Since the program does not exclude partitions with one part, they are included.

Verified locator

• URL: https://oeis.org/A110454
• COMMENTS: Conjecture a(n) = 0 only for n = 1, 2 and 4.
• PROGRAM: 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