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%I #26 Feb 22 2024 09:09:30
%S 1,0,0,121,0,0,0,0,12321,0,0,0,121,0,0,121242121,0,12321,5221225,0,0,
%T 121,0,0,1212225222121,0,12321,5221225,0,0,10201,0,0,1212225222121,0,
%U 12122232623222121
%N Largest palindromic square which is a concatenation of partitions of n; or 0 if no such number exists.
%F a(n) <= A079842(n).
%F If n is a palindromic square, then a(n) >= n.
%e Note that a(4) = a(13) = a(22) = 121 as the digits of 121 can be partitioned as 1+2+1 or 12+1 or 1+21.
%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 A370512(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 q = tuple(Counter(p).elements())
%o c = sum((Counter(str(d)) for d in q), start=Counter())
%o if len(tuple(filter(lambda x:x&1,c.values()))) <= 1:
%o for a in multiset_permutations(q):
%o if (b:=''.join(str(d) for d in a))==b[::-1] and is_square(k:=int(b)):
%o m = max(k,m)
%o if m>0:
%o smax=s
%o return m
%Y Cf. A002779, A079842.
%K nonn,more,base
%O 1,4
%A _Chai Wah Wu_, Feb 20 2024
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