A029781 Squares such that digits of sqrt(n) appear in both n and n^(3/2).

0, 1, 25, 36, 100, 121, 625, 2500, 3025, 3600, 4096, 4356, 5776, 9801, 10000, 10201, 12100, 12321, 12544, 13225, 13456, 15625, 50625, 62500, 75625, 82944, 104329, 141376, 164025, 249001, 250000, 251001, 252004, 275625, 302500

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Programs

Python

from itertools import count, islice
from math import prod
def A029781_gen(): # generator of terms
    return map(lambda x:x[1], filter(lambda x:set(str(x[0])) <= set(str(x[1])) & set(str(prod(x))),((n,n**2) for n in count(0))))
A029781_list = list(islice(A029781_gen(),20)) # Chai Wah Wu, Apr 03 2023

Formula

a(n) = A029780(n)^2. - Sean A. Irvine, Mar 04 2020