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%I #48 Feb 15 2024 01:57:53
%S 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,
%T 51,52,53,55,58,80,81,82,83,85,88,100,101,102,103,105,108,110,111,112,
%U 113,115,118,120,121,122,123,125,128,130,131,132,133,135,138
%N Numbers that are still valid after a horizontal reflection on a calculator display.
%C Note that these numbers may not be unchanged after a horizontal reflection.
%C 2 and 5 are taken as mirror images (as on calculator displays).
%C A007284 is a subsequence.
%C Also, numbers whose all digits are Fibonacci numbers. - _Amiram Eldar_, Feb 15 2024
%H Robert Baillie and Thomas Schmelzer, <a href="https://library.wolfram.com/infocenter/MathSource/7166/">Summing Kempner's Curious (Slowly-Convergent) Series</a>, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
%F Sum_{n>=2} 1/a(n) = 4.887249145579262560308470922947674796541485176473171687107616547235128170930... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 15 2024
%e The sequence begins:
%e 0, 1, 2, 3, 5, 8, 10, 11, 12, 13, ...;
%e 0, 1, 5, 3, 2, 8, 10, 11, 15, 13, ...;
%e 23 has its reflection as 53 in a horizontal mirror.
%e 182 has its reflection as 185 in a horizontal mirror.
%t Select[Range[0, 140], Intersection[IntegerDigits[#], {4, 6, 7, 9}] == {} &] (* _Amiram Eldar_, Nov 17 2018 *)
%o (PARI) a(n, d=[0, 1, 2, 3, 5, 8]) = fromdigits(apply(k -> d[1+k], digits(n-1, #d))) \\ _Rémy Sigrist_, Nov 17 2018
%Y Cf. A000787, A007284, A018846.
%K nonn,base
%O 1,3
%A _Kritsada Moomuang_, Nov 17 2018
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