A359347 Roots of reversible pandigital square numbers.

1111103, 3011111, 11110922, 11111003, 11111030, 11111120, 11111210, 11112110, 11211110, 12111110, 21111110, 21911111, 30011111, 30111110, 101110922, 101111112, 101111121, 101111211, 102111111, 110109212, 110911211, 110921111, 111109220, 111110030, 111110103

Offset: 1

Author

Martin Renner, Dec 27 2022

Keywords

• nonn
• base

Comments

Reversible pandigital square numbers are perfect squares containing each digit from 0 to 9 at least once and still remain square numbers (not necessarily of the same length) when reversing the digits.

Examples

			1111103^2 = 1234549876609 <~> 9066789454321 = 3011111^2.
11110922^2 = 123452587690084  <~> 480096785254321 = 21911111^2.
		

Links

• Martin Renner, Table of n, a(n) for n = 1..458

Crossrefs

Cf. A102859, A359346.

Programs

Python

from math import isqrt
from itertools import count, islice
def c(n): return len(set(s:=str(n)))==10 and isqrt(r:=int(s[::-1]))**2==r
def agen(): yield from (k for k in count(10**6) if c(k*k))
print(list(islice(agen(), 25))) # Michael S. Branicky, Dec 27 2022

Formula

a(n) = sqrt(A359346(n)).