

A321702


Numbers that are still valid after a horizontal reflection on a calculator display.


0



0, 1, 2, 3, 5, 8, 10, 11, 12, 13, 15, 18, 20, 21, 22, 23, 25, 28, 30, 31, 32, 33, 35, 38, 50, 51, 52, 53, 55, 58, 80, 81, 82, 83, 85, 88, 100, 101, 102, 103, 105, 108, 110, 111, 112, 113, 115, 118, 120, 121, 122, 123, 125, 128, 130, 131, 132, 133, 135, 138
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OFFSET

1,3


COMMENTS

Note that these numbers may not be unchanged after a horizontal reflection.
2 and 5 are taken as mirror images (as on calculator displays).
Also, numbers whose all digits are Fibonacci numbers.  Amiram Eldar, Feb 15 2024


LINKS



FORMULA

Sum_{n>=2} 1/a(n) = 4.887249145579262560308470922947674796541485176473171687107616547235128170930... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links).  Amiram Eldar, Feb 15 2024


EXAMPLE

The sequence begins:
0, 1, 2, 3, 5, 8, 10, 11, 12, 13, ...;
0, 1, 5, 3, 2, 8, 10, 11, 15, 13, ...;
23 has its reflection as 53 in a horizontal mirror.
182 has its reflection as 185 in a horizontal mirror.


MATHEMATICA

Select[Range[0, 140], Intersection[IntegerDigits[#], {4, 6, 7, 9}] == {} &] (* Amiram Eldar, Nov 17 2018 *)


PROG

(PARI) a(n, d=[0, 1, 2, 3, 5, 8]) = fromdigits(apply(k > d[1+k], digits(n1, #d))) \\ Rémy Sigrist, Nov 17 2018


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



