A023733 Numbers with no 3's in base-5 expansion.
0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 14, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 39, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 64, 70, 71, 72, 74, 100, 101, 102, 104, 105, 106, 107, 109, 110, 111, 112, 114
Offset: 1
Examples
14 in base 5 is 24, which contains no 3's, so 14 is in the sequence. 15 in base 5 is 30, so 15 is not in the sequence.
Links
- Nathaniel Johnston, Table of n, a(n) for n = 1..10000
- Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
- Index entries for 5-automatic sequences.
Programs
-
Maple
seq(`if`(numboccur(3,convert(n,base,5))=0,n,NULL),n=0..127); # Nathaniel Johnston, Jun 27 2011
-
Mathematica
Select[Range[0, 124], Count[IntegerDigits[#, 5], 3] == 0 &] Select[Range[0,200],DigitCount[#,5,3]==0&] (* Harvey P. Dale, Jul 29 2024 *)
-
PARI
is(n)=while(n>3, if(n%5==3, return(0)); n\=5); 1 \\ Charles R Greathouse IV, Feb 12 2017
-
Scala
(0 to 124).filter(Integer.toString(, 5).indexOf("3") == -1) // _Alonso del Arte, Feb 05 2019
Formula
Sum_{n>=2} 1/a(n) = 7.2918685472993284072384543509909968409572571215800451577936556651148540560895813691253670323741759722063... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Apr 14 2025