A023721 -id:A023721 - cp's OEIS frontend

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

Olivier Gérard

			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.

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.

Cf. A020654, A023721, A023725, A023729.

seq(`if`(numboccur(3,convert(n,base,5))=0,n,NULL),n=0..127); # Nathaniel Johnston, Jun 27 2011

Select[Range[0, 124], Count[IntegerDigits[#, 5], 3] == 0 &]
Select[Range[0,200],DigitCount[#,5,3]==0&] (* Harvey P. Dale, Jul 29 2024 *)

is(n)=while(n>3, if(n%5==3, return(0)); n\=5); 1 \\ Charles R Greathouse IV, Feb 12 2017

(0 to 124).filter(Integer.toString(, 5).indexOf("3") == -1) // _Alonso del Arte, Feb 05 2019

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

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

Original entry on oeis.org

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

Olivier Gérard

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.

Cf. A020654, A023721, A023729, A023733.

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

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

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

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

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

Original entry on oeis.org

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

Olivier Gérard

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.

Cf. A020654, A023721, A023725, A023733.

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

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

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

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

A382415 Numbers with at least one zero in their base-5 representation.

Original entry on oeis.org

0, 5, 10, 15, 20, 25, 26, 27, 28, 29, 30, 35, 40, 45, 50, 51, 52, 53, 54, 55, 60, 65, 70, 75, 76, 77, 78, 79, 80, 85, 90, 95, 100, 101, 102, 103, 104, 105, 110, 115, 120, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145

Offset: 1

Paolo Xausa, Mar 25 2025

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. analogous sequences in other bases: A062289 (base 2), A081605 (base 3), A196032 (base 4), A382416 (base 6), A382413 (base 7), A382417 (base 8), A382418 (base 9), A011540 (base 10).

Cf. A007091, A023721 (complement), A023722.

Select[Range[0, 150], DigitCount[#, 5, 0] > 0 &]

A249102 Numbers with no 1's in base-7 expansion.

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 98, 100, 101, 102, 103, 104, 112, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 126, 128, 129, 130, 131, 132, 133

Offset: 1

Zak Seidov, Oct 21 2014

			14_10 = 20_7, 16_10 = 22_10, 17_10 = 23_7.
14 in base 7 is 20, which contains no 1s, so 14 is in the sequence.
15 in base 7 is 21, which contains one 1, so 15 is not in the sequence.
16 in base 7 is 22, so 16 is in the sequence.

G. C. Greubel, Table of n, a(n) for n = 1..5000

Subsequence of A047306. Cf. A023721, A023725, A023729, A023733, A005823. This sequence has no terms in common with A016993.

Select[Range[0, 200], FreeQ[IntegerDigits[#, 7], 1] &] (* Seidov *)
Select[Range[0, 139], DigitCount[#, 7, 1] == 0 &] (* Alonso del Arte, Oct 26 2014 *)

fromdigits(v, b=10)=subst(Pol(v), 'x, b) \\ needed for gp < 2.63 or so
a(n)=a(n)=fromdigits(apply(k->if(k, k+1, 0), digits(n, 6)),7) \\ Charles R Greathouse IV, Oct 30 2014

A382412 Numbers with no zeros in their base-7 representation.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90

Offset: 1

Paolo Xausa, Mar 24 2025

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. zeroless numbers in other bases: A126646 (base 2), A032924 (base 3), A023705 (base 4), A023721 (base 5), A248910 (base 6), A255805 (base 8), A255808 (base 9), A052382 (base 10).

Cf. A007093, A043393, A249102, A382413 (complement).

Select[Range[100], DigitCount[#, 7, 0] == 0 &]

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A382412 Numbers with no zeros in their base-7 representation.

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