A023729 Numbers with no 2's in their base-5 expansion.

0, 1, 3, 4, 5, 6, 8, 9, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 40, 41, 43, 44, 45, 46, 48, 49, 75, 76, 78, 79, 80, 81, 83, 84, 90, 91, 93, 94, 95, 96, 98, 99, 100, 101, 103, 104, 105, 106, 108, 109, 115, 116, 118, 119, 120, 121

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• base
• easy

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.

Crossrefs

Cf. A020654, A023721, A023725, A023733.

Programs

Maple

seq(`if`(numboccur(2,convert(n,base,5))=0,n,NULL),n=0..127); # Nathaniel Johnston, Jun 27 2011

Mathematica

Select[ Range[ 0, 125 ], (Count[ IntegerDigits[ #, 5 ], 2 ]==0)& ]
Select[Range[0, 120], DigitCount[#, 5, 2] == 0 &] (* Amiram Eldar, Apr 14 2025 *)

PARI

is(n)=while(n>2, if(n%5==2, return(0)); n\=5); 1 \\ Charles R Greathouse IV, Feb 12 2017

Formula

Sum_{n>=2} 1/a(n) = 6.4926328481629227744899858111920644967528391159751448517967690160220746453627777857879224296518328062481... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Apr 14 2025