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%I #35 Jan 01 2021 12:28:42
%S 0,1,9,16,81,169,196,961,1089,1681,6889,9801,10609,10816,11881,19881,
%T 61009,69169,69696,80089,90601,91809,110889,160801,190096,190969,
%U 198916,199809,609961,660969,698896,811801,896809,900601,910116,919681,998001,1006009
%N Rotationally ambigrammatic square numbers with no trailing zeros.
%C A rotationally ambigrammatic number (A045574) is one that can be rotated by 180 degrees resulting in a readable, most often new number. Such numbers, by definition, can only contain the digits 0, 1, 6, 8, 9.
%C If the number once rotated happens to be the same number (e.g., 6889) it is a strobogrammatic number. Those present here are the terms of A018848.
%C Numbers such as 100, which is a square with trailing zeros, have been excluded. Such numbers rotated by 180 degrees would be written with leading zeros. Typically this is not the way we write numbers.
%C This sequence is infinite as it contains (10^k + 3)^2 and (3*10^k + 1)^2 for any k >= 0 (note also that A004086((10^k + 3)^2) = (3*10^k + 1)^2 when k > 0). - _Rémy Sigrist_, Dec 30 2020
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ambigram">Ambigram</a>
%F a(n) = A339996(n)^2.
%t Select[Range[0, 1000], (# == 0 || ! Divisible[#, 10]) && AllTrue[IntegerDigits[#^2], MemberQ[{0, 1, 6, 8, 9}, #1] &] &]^2 (* _Amiram Eldar_, Dec 30 2020 *)
%o (PARI) isra(n) = (n%10) && (!setminus(Set(Vec(Str(n))), Vec("01689"))) || !n; \\ A045574
%o isok(n) = issquare(n) && isra(n); \\ _Michel Marcus_, Dec 30 2020
%Y Intersection of A045574 and A000290.
%Y Cf. A004086, A339996 (square roots).
%K nonn,base,easy
%O 1,3
%A _Philip Mizzi_, Dec 30 2020
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