A321702 Numbers that are still valid after a horizontal reflection on a calculator display.

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

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