A079842 Largest square which is a concatenation of partitions of n; or 0 if no such number exists.

1, 0, 0, 121, 0, 0, 25, 0, 12321, 2116, 0, 0, 5112121, 0, 0, 121242121, 0, 1121513121, 2511112321, 0, 0, 213223221121, 0, 0, 1212111311221321, 0, 4231211211113121, 1111111222222225, 0, 0, 111131111122142224, 0, 0, 11111111122222222225

Offset

1,4

Links

Table of n, a(n) for n=1..34.

Formula

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

Example

a(4) = 121 though 4 itself is a square. a(7) = 25 (16 is also a square).

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 A079842(n):
    smax, m = 0, 0
    for s, p in sorted(partitions(n, size=True), key=itemgetter(0), reverse=True):
        if s<smax:
            break
        for a in multiset_permutations(Counter(p).elements()):
            if is_square(k:=int(''.join(str(d) for d in a))):
                m = max(k, m)
        if m>0:
            smax=s
    return m # Chai Wah Wu, Feb 20 2024

Crossrefs

Sequence in context: A106547 A106544 A370512 * A014756 A014748 A334058

Adjacent sequences: A079839 A079840 A079841 * A079843 A079844 A079845

Keyword

base,more,nonn

Author

Amarnath Murthy, Feb 16 2003

Extensions

More terms from Michel ten Voorde Jun 20 2003

a(23)-a(32) from Chai Wah Wu, Feb 20 2024

a(33)-a(34) from Chai Wah Wu, Feb 21 2024

Status

approved