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%I #17 Feb 21 2024 14:42:35
%S 1,0,0,121,0,0,25,0,12321,2116,0,0,5112121,0,0,121242121,0,1121513121,
%T 2511112321,0,0,213223221121,0,0,1212111311221321,0,4231211211113121,
%U 1111111222222225,0,0,111131111122142224,0,0,11111111122222222225
%N Largest square which is a concatenation of partitions of n; or 0 if no such number exists.
%F If n is square, then a(n) >= n.
%e a(4) = 121 though 4 itself is a square. a(7) = 25 (16 is also a square).
%o (Python)
%o from collections import Counter
%o from operator import itemgetter
%o from sympy.ntheory.primetest import is_square
%o from sympy.utilities.iterables import partitions, multiset_permutations
%o def A079842(n):
%o smax, m = 0, 0
%o for s, p in sorted(partitions(n,size=True),key=itemgetter(0),reverse=True):
%o if s<smax:
%o break
%o for a in multiset_permutations(Counter(p).elements()):
%o if is_square(k:=int(''.join(str(d) for d in a))):
%o m = max(k,m)
%o if m>0:
%o smax=s
%o return m # _Chai Wah Wu_, Feb 20 2024
%K base,more,nonn
%O 1,4
%A _Amarnath Murthy_, Feb 16 2003
%E More terms from _Michel ten Voorde_ Jun 20 2003
%E a(23)-a(32) from _Chai Wah Wu_, Feb 20 2024
%E a(33)-a(34) from _Chai Wah Wu_, Feb 21 2024
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