A340164 Rotationally ambigrammatic square numbers with no trailing zeros.

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

Author

Philip Mizzi, Dec 30 2020

Keywords

• nonn
• base
• easy

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

Links

• Wikipedia, Ambigram

Crossrefs

Intersection of A045574 and A000290.

Cf. A004086, A339996 (square roots).

Programs

Mathematica

Select[Range[0, 1000], (# == 0 || ! Divisible[#, 10]) && AllTrue[IntegerDigits[#^2], MemberQ[{0, 1, 6, 8, 9}, #1] &] &]^2 (* Amiram Eldar, Dec 30 2020 *)

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

Formula

a(n) = A339996(n)^2.