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

1,3

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.

Formula

Sum_{n>=2} 1/a(n) = 7.2918685472993284072384543509909968409572571215800451577936556651148540560895813691253670323741759722063... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Apr 14 2025

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A020654, A023721, A023725, A023729.

Sequence in context: A349829 A230633 A024616 * A380699 A154112 A039101

Adjacent sequences: A023730 A023731 A023732 * A023734 A023735 A023736

Keyword

nonn,base,easy

Author

Olivier Gérard

Status

approved