A356417 Numbers whose reversal is a square.

0, 1, 4, 9, 10, 18, 40, 46, 52, 61, 63, 90, 94, 100, 121, 144, 148, 163, 169, 180, 400, 423, 441, 460, 484, 487, 520, 522, 526, 610, 630, 652, 675, 676, 691, 900, 925, 927, 940, 961, 982, 1000, 1042, 1062, 1089, 1210, 1251, 1273, 1297, 1405, 1426, 1440, 1480

Offset

1,3

Comments

Every power of 10 is a term in the sequence.

If k is in the sequence then so is 10*k. - David A. Corneth, Aug 06 2022

If all multiples of 10 were omitted, A074896 would result. - Jon E. Schoenfield, Aug 06 2022

Links

Table of n, a(n) for n=1..53.

Example

0 is a term, 0 -> 0 (0^2).
10 is a term, 10 -> 01 (leading zero is dropped) (1^2).
691 is a term, 691 -> 196 (14^2).
1800 is a term, 1800 -> 0081 (leading zeros are dropped) (9^2).

Mathematica

Select[Range[0, 1500], IntegerQ[Sqrt[IntegerReverse[#]]] &] (* Amiram Eldar, Aug 06 2022 *)

Prog

(Python)
from sympy import integer_nthroot
def ok(n):
    return integer_nthroot(int(str(n)[::-1]), 2)[1]
print([k for k in range(1500) if ok(k)])
(Python)
from math import isqrt
from itertools import count, islice
def A356417_gen(): # generator of terms
    yield 0
    for l in count(1):
        nlist = []
        for m in range(1, isqrt(10**l)+1):
            if m%10:
                s = str(m**2)
                nlist.append(int(s[::-1])*10**(l-len(s)))
        yield from sorted(nlist)
A356417_list = list(islice(A356417_gen(), 100)) # Chai Wah Wu, Aug 07 2022
(PARI) isok(k) = issquare(fromdigits(Vecrev(digits(k)))); \\ Michel Marcus, Aug 06 2022

Crossrefs

Cf. A002942, A004086, A074896.

Sequence in context: A236652 A236748 A102837 * A004631 A316113 A336256

Adjacent sequences: A356414 A356415 A356416 * A356418 A356419 A356420

Keyword

nonn,base

Author

Daniel Blam, Aug 06 2022

Status

approved