A275028 Squares whose digital rotation is also a square.

1, 121, 196, 529, 625, 961, 6889, 10201, 69169, 1002001, 1022121, 1212201, 5221225, 100020001, 100220121, 109181601, 121022001, 522808225, 602555209, 10000200001, 10002200121, 10020210201, 10201202001, 12100220001, 62188888129, 1000002000001

Offset

1,2

Comments

From Jon E. Schoenfield, Nov 13 2016: (Start)

It is assumed that the rotation changes each digit 6 to a 9 and vice versa, and that the digits 0, 1, 2, 5, and 8 are unchanged by the rotation, as is the case with a seven-segment display in which the digits are formed basically as follows:

. _ _ _ _ _ _ _ _

| | | _| _| |_| |_ |_ | |_| |_|

|_| | |_ _| | _| |_| | |_| _|

(End)

Sequence is infinite since (10^m+1)^2 for m>0 are terms. Leading zeros after rotation are not allowed, as otherwise 10^m would be terms. All terms start and end with digits 1, 5, 6 or 9. - Chai Wah Wu, Apr 09 2024

Links

Chai Wah Wu, Table of n, a(n) for n = 1..164

Prime Curios, 31

Example

961 becomes 196 under such a rotation.

Mathematica

Select[Range[10^6]^2, If[Or[IntersectingQ[#, {3, 4, 7}], Last@# == 0], False, IntegerQ@ Sqrt@ FromDigits[Reverse@ # /. {6 -> 9, 9 -> 6}]] &@ IntegerDigits@ # &] (* Michael De Vlieger, Nov 14 2016 *)

Prog

(Python)
from itertools import count, islice
from sympy.ntheory.primetest import is_square
def A275028_gen(): # generator of terms
    r, t = ''.maketrans('69', '96'), set('0125689')
    for l in count(1):
        if l%10:
            m = l**2
            if set(s:=str(m)) <= t and is_square(int(s[::-1].translate(r))):
                yield m
A275028_list = list(islice(A275028_gen(), 10)) # Chai Wah Wu, Apr 09 2024

Crossrefs

Cf. A178316.

Sequence in context: A268519 A364778 A037050 * A036309 A346507 A119378

Adjacent sequences: A275025 A275026 A275027 * A275029 A275030 A275031

Keyword

nonn,base

Author

Seiichi Manyama, Nov 12 2016

Status

approved