A370512 Largest palindromic square which is a concatenation of partitions of n; or 0 if no such number exists.

1, 0, 0, 121, 0, 0, 0, 0, 12321, 0, 0, 0, 121, 0, 0, 121242121, 0, 12321, 5221225, 0, 0, 121, 0, 0, 1212225222121, 0, 12321, 5221225, 0, 0, 10201, 0, 0, 1212225222121, 0, 12122232623222121

Offset

1,4

Links

Table of n, a(n) for n=1..36.

Formula

a(n) <= A079842(n).

If n is a palindromic square, then a(n) >= n.

Example

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.

Prog

(Python)
from collections import Counter
from operator import itemgetter
from sympy.ntheory.primetest import is_square
from sympy.utilities.iterables import partitions, multiset_permutations
def A370512(n):
    smax, m = 0, 0
    for s, p in sorted(partitions(n, size=True), key=itemgetter(0), reverse=True):
        if s<smax:
            break
        q = tuple(Counter(p).elements())
        c = sum((Counter(str(d)) for d in q), start=Counter())
        if len(tuple(filter(lambda x:x&1, c.values()))) <= 1:
            for a in multiset_permutations(q):
                if (b:=''.join(str(d) for d in a))==b[::-1] and is_square(k:=int(b)):
                    m = max(k, m)
            if m>0:
                smax=s
    return m

Crossrefs

Cf. A002779, A079842.

Sequence in context: A033187 A106547 A106544 * A079842 A014756 A014748

Adjacent sequences: A370509 A370510 A370511 * A370513 A370514 A370516

Keyword

nonn,more,base

Author

Chai Wah Wu, Feb 20 2024

Status

approved