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A339996 Numbers whose square is rotationally ambigrammatic with no trailing zeros. 1
0, 1, 3, 4, 9, 13, 14, 31, 33, 41, 83, 99, 103, 104, 109, 141, 247, 263, 264, 283, 301, 303, 333, 401, 436, 437, 446, 447, 781, 813, 836, 901, 947, 949, 954, 959, 999, 1003, 1004, 1009, 1053, 1054, 1291, 1349, 1367, 2467, 2486, 2609, 2849, 2949, 2986, 3001 (list; graph; refs; listen; history; text; internal format)
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 it is a strobogrammatic number (A000787); such numbers form a subset of the ambigrammatic numbers.

Numbers (such as 10) whose square has trailing zeros have been excluded because the rotation of such a number by 180 degrees would result in a number with leading zeros. Typically this is not the way we write numbers.

The numbers 14 and 31 are interesting numbers in this sequence in that when their square is rotated 180 degrees, the square root results in the other number. I believe this is unique to only these two numbers.

LINKS

Table of n, a(n) for n=1..52.

Wikipedia, Ambigram

FORMULA

a(n) = sqrt(A340164(n)).

EXAMPLE

13^2 = 169. A rotationally ambigrammatic number. Hence, 13 is a term.

15^2 = 225. Not rotationally ambigrammatic and hence 15 is not a term.

10^2 = 100. This number has trailing zeros, so under this definition of rotationally ambigrammatic, 10 is not a term.

MATHEMATICA

Select[Range[0, 4001], (# == 0 || !Divisible[#, 10]) && AllTrue[IntegerDigits[#^2], MemberQ[{0, 1, 6, 8, 9}, #1] &] &] (* Amiram Eldar, Dec 26 2020 *)

PROG

(PARI) isra(n) = (n%10) && (!setminus(Set(Vec(Str(n))), Vec("01689"))) || !n; \\ A045574

isok(n) = isra(n^2); \\ Michel Marcus, Dec 27 2020

CROSSREFS

Cf. A045574, A340164 (squares).

Sequence in context: A249179 A103014 A116552 * A225288 A167930 A326981

Adjacent sequences:  A339993 A339994 A339995 * A339997 A339998 A340000

KEYWORD

nonn,base

AUTHOR

Philip Mizzi, Dec 25 2020

STATUS

approved

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Last modified June 12 06:52 EDT 2021. Contains 344943 sequences. (Running on oeis4.)