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 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 (list; graph; refs; listen; history; text; internal format)
 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). A007284 is a subsequence. Also, numbers whose all digits are Fibonacci numbers. - Amiram Eldar, Feb 15 2024 LINKS Table of n, a(n) for n=1..60. Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008. 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(n-1, #d))) \\ Rémy Sigrist, Nov 17 2018 CROSSREFS Cf. A000787, A007284, A018846. Sequence in context: A331864 A272669 A028770 * A351876 A028800 A028841 Adjacent sequences: A321699 A321700 A321701 * A321703 A321704 A321705 KEYWORD nonn,base AUTHOR Kritsada Moomuang, Nov 17 2018 STATUS approved

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Last modified August 15 07:32 EDT 2024. Contains 375173 sequences. (Running on oeis4.)