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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Nov 12 2016
STATUS
approved