A023725 Numbers with no 1's in their base-5 expansion.

0, 2, 3, 4, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 50, 52, 53, 54, 60, 62, 63, 64, 65, 67, 68, 69, 70, 72, 73, 74, 75, 77, 78, 79, 85, 87, 88, 89, 90, 92, 93, 94, 95, 97, 98, 99, 100, 102, 103, 104, 110, 112, 113, 114, 115, 117, 118, 119, 120

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, A023729, A023733.

Programs

Maple

seq(`if`(numboccur(1,convert(n,base,5))=0,n,NULL),n=0..127); # Nathaniel Johnston, Jun 27 2011

Mathematica

Select[ Range[ 0, 125 ], (Count[ IntegerDigits[ #, 5 ], 1 ]==0)& ]
Select[Range[0, 120], DigitCount[#, 5, 1] == 0 &] (* Amiram Eldar, Apr 14 2025 *)

PARI

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

Formula

Sum_{n>=2} 1/a(n) = 4.7113203882192880160403245816366085015069192113921100121384809791433027046475062716543062654277431569224... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Apr 14 2025