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A340164
Rotationally ambigrammatic square numbers with no trailing zeros.
1
0, 1, 9, 16, 81, 169, 196, 961, 1089, 1681, 6889, 9801, 10609, 10816, 11881, 19881, 61009, 69169, 69696, 80089, 90601, 91809, 110889, 160801, 190096, 190969, 198916, 199809, 609961, 660969, 698896, 811801, 896809, 900601, 910116, 919681, 998001, 1006009
OFFSET
1,3
COMMENTS
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.
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.
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.
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
FORMULA
a(n) = A339996(n)^2.
MATHEMATICA
Select[Range[0, 1000], (# == 0 || ! Divisible[#, 10]) && AllTrue[IntegerDigits[#^2], MemberQ[{0, 1, 6, 8, 9}, #1] &] &]^2 (* Amiram Eldar, Dec 30 2020 *)
PROG
(PARI) isra(n) = (n%10) && (!setminus(Set(Vec(Str(n))), Vec("01689"))) || !n; \\ A045574
isok(n) = issquare(n) && isra(n); \\ Michel Marcus, Dec 30 2020
CROSSREFS
Intersection of A045574 and A000290.
Cf. A004086, A339996 (square roots).
Sequence in context: A375501 A167349 A267763 * A308248 A179307 A014720
KEYWORD
nonn,base,easy
AUTHOR
Philip Mizzi, Dec 30 2020
STATUS
approved