A321702 - OEIS

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

(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.