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

Author

Chai Wah Wu, Feb 20 2024

Keywords

• nonn
• more
• base

Examples

			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.
		

Crossrefs

Cf. A002779, A079842.

Programs

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 s0:
                smax=s
    return m

Formula

a(n) <= A079842(n).

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