A007095 -id:A007095 - cp's OEIS frontend

A052419 Numbers without 7 as a digit.

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 80, 81, 82, 83, 84, 85, 86, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits OEIS wiki, Jan 12 2020.
Index entries for 10-automatic sequences.

Cf. A004182, A004726, A038615 (subset of primes), A082836 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052421 (without 8), A007095 (without 9).

a052419 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 6 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 7 in Intseq(n) ]; // Bruno Berselli, May 28 2011

a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<7, d, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

Select[Range[100],DigitCount[#,10,7]==0&] (* Harvey P. Dale, Aug 23 2011 *)

lista(nn)=for (n=0, nn, if (!vecsearch(vecsort(digits(n),,8), 7), print1(n, ", "));); \\ Michel Marcus, Feb 22 2015

/* See OEIS wiki page for more programs. */
apply( {A052419(n)=fromdigits(apply(d->d+(d>6),digits(n-1,9)))}, [1..99]) \\ a(n)
select( {is_A052419(n)=!setsearch(Set(digits(n)),7)}, [0..99]) \\ used in A038615
next_A052419(n, d=digits(n+=1))={for(i=1,#d, d[i]==7&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used in A038615. - M. F. Hasler, Jan 11 2020

from gmpy2 import digits
def A052419(n): return int(digits(n-1,9).replace('8','9').replace('7','8')) # Chai Wah Wu, Jun 28 2025

seq 0 1000 | grep -v 7; # Joerg Arndt, May 29 2011

a(n) = replace digits d > 6 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{n>1} 1/a(n) = A082836 = 22.493475... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 13 2020

Offset changed by Reinhard Zumkeller, Oct 07 2014

A171397 Write n in base 10, but then read it as if it were written in base 11: if n = Sum_{i >= 0} d_i10^i, with 0 <= d_i <= 9, then a(n) = Sum_{i >= 0} d_i11^i.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72

Offset: 0

Paul Weisenhorn, Jul 11 2011

This is the sequence of all decimal integers that are created when base 10 numbers are interpreted as base 11 numbers.
Numbers without digit A (=10) in their representation in base 11. Complement of A095778. - François Marques, Oct 20 2020
Original definition: Earliest sequence containing no 11-term arithmetic progression.
In general, if p is prime, the earliest sequence containing no p-term arithmetic progression is created when base (p-1) numbers are interpreted as base p numbers.

			a(53)=58 because 53_11 in base 11 equals 58. - _François Marques_, Oct 20 2020

D. E. Arganbright, Mathematical Modeling with Spreadsheets, ABACUS, Vol. 3, #4(1986), 19-31.

François Marques, Table of n, a(n) for n = 0..10000

Different from A065039. - Alois P. Heinz, Sep 07 2011
CNumbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Numbers with no digit b-1 in base b : A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), this sequence (b=11).

seq(`if`(numboccur (10, convert (n, base, 11))=0, n, NULL), n=0..122);
# second Maple program:
a:= n-> (l-> add(l[i]*11^(i-1), i=1..nops(l)))(convert(n, base, 10)):
seq(a(n), n=0..66);  # Alois P. Heinz, Aug 30 2024

Table[FromDigits[RealDigits[n, 10], 11], {n, 0, 100}] (* François Marques, Oct 20 2020 *)

a(n) = fromdigits(digits(n), 11); \\ Michel Marcus, Oct 09 2020

def A171397(n): return int(str(n),11) # Chai Wah Wu, Aug 30 2024

Edited by N. J. A. Sloane, Aug 31 2024

A037465 a(n) = Sum_{i=0..m} d(i)6^i, where Sum_{i=0..m} d(i)5^i is the base 5 representation of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93

Offset: 0

Clark Kimberling

Numbers without digit 5 in base 6. Complement of A333656. - François Marques, Oct 13 2020

			a(34)=46 because 34 is 114_5 in base 5 and 114_6=46. - _François Marques_, Oct 13 2020

François Marques, Table of n, a(n) for n = 0..10000 (first 1000 terms from Clark Kimberling)

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).

Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), this sequence (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Table[FromDigits[RealDigits[n, 5], 6], {n, 0, 100}] (* Clark Kimberling, Aug 14 2012 *)

a(n) = fromdigits(digits(n, 5), 6); \\ François Marques, Oct 13 2020

from gmpy2 import digits
def A037465(n): return int(digits(n,5),6) # Chai Wah Wu, May 06 2025

Offset changed to 0 by Clark Kimberling, Aug 14 2012

A052406 Numbers without 4 as a digit.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

This is a frequent sequence on Chinese, Japanese and Korean elevator buttons. - Jean-Sebastien Girard (circeus(AT)hotmail.com), Jul 28 2008

Essentially numbers in base 9 (using digits 0, 1, 2, 3, 5, 6, 7, 8, 9 rather than 0-8). - Charles R Greathouse IV, Oct 13 2013

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits OEIS wiki, Jan 12 2020.
Eric Weisstein's World of Mathematics, Uban Number
Wikipedia, Tetraphobia.
Index entries for 10-automatic sequences.

Cf. A004179, A004723, A011760, A038612 (subset of primes), A082833 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

a052406 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 3 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 4 in Intseq(n) ]; // Bruno Berselli, May 28 2011

a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<4, d, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

Select[Range[100], DigitCount[#, 10, 4] == 0 &] (* Alonso del Arte, Oct 13 2013 *)

g(n)= local(x,v,j,flag); for(x=1,n, v=Vec(Str(x)); flag=1; for(j=1,length(v), if(v[j]=="4",flag=0)); if(flag,print1(x",") ) ) \\ Cino Hilliard, Apr 01 2007

apply( {A052406(n)=fromdigits(apply(d->d+(d>3),digits(n-1,9)))}, [1..99]) \\ a(n)
select( {is_A052406(n)=!setsearch(Set(digits(n)),4)}, [0..99]) \\ Used in A038612
next_A052406(n, d=digits(n+=1))={for(i=1, #d, d[i]!=4|| return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used for A038612. - M. F. Hasler, Jan 11 2020

def A052406(n): n-=1; return sum((d+(d>3))*10**i for d,i in ((n//9**i%9,i) for i in range(math.ceil(math.log(n+1,9))))) # M. F. Hasler, Jan 13 2020

from gmpy2 import digits
def A052406(n): return int(digits(n-1,9).translate(str.maketrans('45678','56789'))) # Chai Wah Wu, Jun 28 2025

seq 0 1000 | grep -v 4; # Joerg Arndt, May 29 2011

a(n) = replace digits d > 3 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{k>1} 1/a(k) = A082833 = 21.327465... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 13 2020

Offset changed by Reinhard Zumkeller, Oct 07 2014

A338090 Numbers having at least one 8 in their representation in base 9.

Original entry on oeis.org

8, 17, 26, 35, 44, 53, 62, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 89, 98, 107, 116, 125, 134, 143, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 170, 179, 188, 197, 206, 215, 224, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 251, 260, 269, 278, 287, 296, 305, 314, 315

Offset: 1

François Marques, Oct 09 2020

Blocks of consecutive terms have lengths in A002452. - Devansh Singh, Oct 21 2020

			70 is not in the sequence since it is 77_9 in base 9, but 76 is in the sequence since it is 84_9 in base 9.

François Marques, Table of n, a(n) for n = 1..10000

Cf. A007095 (base 9).
Complement of A037477.
Cf. A043485 (numbers with exactly one 8 in base 9).
Cf. Numbers with at least one digit b-1 in base b: A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), this sequence (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

seq(`if`(numboccur(8, convert(n, base, 9))>0, n, NULL), n=0..100);

Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 9 ], 8 ]>0)& ]

isok(m) = #select(x->(x==8), digits(m, 9)) >= 1;

from gmpy2 import digits
def A338090(n):
    def f(x):
        l = (s:=digits(x,9)).find('8')
        if l >= 0: s = s[:l]+'7'*(len(s)-l)
        return n+int(s,8)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A037474 a(n) = Sum{d(i)8^i: i=0,1,...,m}, where Sum{d(i)7^i: i=0,1,...,m} is the base 7 representation of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85

Offset: 0

Clark Kimberling

Numbers without digit 7 in base 8. Complement of A337239. - François Marques, Oct 13 2020

			a(48)=54 because 48 is 66_7 in base 7 and 66_8=54. - _François Marques_, Oct 13 2020

François Marques, Table of n, a(n) for n = 0..10000 (first 1000 terms from Clark Kimberling)

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).

Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), this sequence (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Table[FromDigits[RealDigits[n, 7], 8], {n, 0, 100}] (* Clark Kimberling, Aug 14 2012 *)

a(n) = fromdigits(digits(n, 7), 8); \\ François Marques, Oct 13 2020

from gmpy2 import digits
def A037474(n): return int(digits(n,7),8) # Chai Wah Wu, Dec 04 2024

Offset changed to 0 by Clark Kimberling, Aug 14 2012

A037477 a(n) = Sum{d(i)9^i: i=0,1,...,m}, where Sum{d(i)8^i: i=0,1,...,m} is the base 8 representation of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 81, 82, 83, 84, 85

Offset: 0

Clark Kimberling

Numbers that do not contain the digit 8 in their base 9 expansion. - M. F. Hasler, Oct 05 2014

			a(63) = 7*9+7 = 70 since 63 = 77[8], i.e., "77" when written in base 8;
a(64) = 1*9^2 = 81 since 64 = 100[8]. - _M. F. Hasler_, Oct 05 2014

François Marques, Table of n, a(n) for n = 0..10000 (first 1000 terms from Clark Kimberling)

Cf. A248375.
Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), this sequence (b=9), A007095 (b=10), A171397 (b=11).

Table[FromDigits[RealDigits[n, 8], 9], {n, 0, 100}]
Select[Range[0,100],DigitCount[#,9,8]==0&] (* Harvey P. Dale, Aug 06 2024 *)

a(n) = vector(#n=digits(n,8),i,9^(#n-i))*n~ \\ M. F. Hasler, Oct 05 2014

a(n) = fromdigits(digits(n, 8), 9); \\ François Marques, Oct 15 2020

def A037477(n): return int(oct(n)[2:],9) # Chai Wah Wu, Jan 27 2025

For n<64, a(n) = floor(9n/8) = A248375(n). - M. F. Hasler, Oct 05 2014

Offset changed to 0 by Clark Kimberling, Aug 14 2012

A052404 Numbers without 2 as a digit.

Original entry on oeis.org

0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

M. J. Halm, Word Weirdness, Mpossibilities 66 (Feb. 1998), p. 5.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. J. Halm, Games
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
Index entries for 10-automatic sequences.

Cf. A004177, A004721, A072809, A082831 (Kempner series).
Cf. A052382 (without 0), A052383 (without 1), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).
See A038604 for the subset of primes. - M. F. Hasler, Jan 11 2020

a052404 = f . subtract 1 where
   f 0 = 0
   f v = 10 * f w + if r > 1 then r + 1 else r  where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 2 in Intseq(n) ];  // Bruno Berselli, May 28 2011

a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<2, d, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

ban2Q[n_]:=FreeQ[IntegerDigits[n],2]==True; Select[Range[0,89],ban2Q[#] &] (* Jayanta Basu, May 17 2013 *)
Select[Range[0,100],DigitCount[#,10,2]==0&] (* Harvey P. Dale, Apr 13 2015 *)

lista(nn, d=2) = {for (n=0, nn, if (!vecsearch(vecsort(digits(n),,8),d), print1(n, ", ")););} \\ Michel Marcus, Feb 21 2015

apply( {A052404(n)=fromdigits(apply(d->d+(d>1),digits(n-1,9)))}, [1..99])
next_A052404(n, d=digits(n+=1))={for(i=1, #d, d[i]==2&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n: if there's a digit 2 in n+1, replace the first occurrence by 3 and all following digits by 0.
(A052404_vec(N)=vector(N, i, N=if(i>1, next_A052404(N))))(99) \\ first N terms
select( {is_A052404(n)=!setsearch(Set(digits(n)),2)}, [0..99])
(A052404_upto(N)=select( is_A052404, [0..N]))(99) \\ M. F. Hasler, Jan 11 2020

from gmpy2 import digits
def A052404(n): return int(''.join(str(int(d)+1) if d>'1' else d for d in digits(n-1,9))) # Chai Wah Wu, Aug 30 2024

seq 0 1000 | grep -v 2; # Joerg Arndt, May 29 2011

If the offset were changed to 0: a(0) = 0, a(n+1) = f(a(n)+1,a(n)+1) where f(x,y) = if x<10 and x<>2 then y else if x mod 10 = 2 then f(y+1,y+1) else f(floor(x/10),y). - Reinhard Zumkeller, Mar 02 2008
a(n) = replace digits d > 1 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
Sum_{k>1} 1/a(k) = A082831 = 19.257356... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 14 2020

Offset changed by Reinhard Zumkeller, Oct 07 2014

A095778 Values of n for which A095777(n) is 9 (those terms which are expressible in decimal digits for bases 2 through 10, but not for base 11).

Original entry on oeis.org

10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 131, 142, 153, 164, 175, 186, 197, 208, 219, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 252, 263, 274, 285, 296, 307, 318, 329, 340, 351, 352, 353

Offset: 1

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jun 05 2004

Numbers with at least one digit A (=10) in their representation in base 11. Complementary sequence to A171397. - François Marques, Oct 11 2020

			a(5)=54 because 54 when expressed in successive bases starting at 2 will produce its first non-decimal digit at base 11. Like so: 110110, 2000, 312, 204, 130, 105, 66, 60, 54. In base 11, 54 is 4A.

François Marques, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A095777.
Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), this sequence (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

S := []; for n from 1 to 1000 do; if 1>0 then; ct := 0; ok := true; b := 2; if (n>9) then; while ok=true do; L := convert(n, base, b); for e in L while ok=true do; if (e > 9) then ok:=false; fi; od; if ok=true then; ct := ct + 1; b := b + 1; fi; od; fi; if ct=9 then S := [op(S), n]; fi; fi; od; S;
# or
seq(`if`(numboccur(10, convert(n, base, 11))>0, n, NULL), n=0..1000); # François Marques, Oct 11 2020

Select[Range[400],Max[IntegerDigits[#,11]]>9&] (* Harvey P. Dale, Sep 30 2018 *)

isok(m) = #select(x->(x==10), digits(m, 11)) >= 1; \\ François Marques, Oct 11 2020

from gmpy2 import digits
def A095778(n):
    def f(x):
        l = (s:=digits(x,11)).find('a')
        if l >= 0: s = s[:l]+'9'*(len(s)-l)
        return n+int(s)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

A337250 Numbers having at least one 3 in their representation in base 4.

Original entry on oeis.org

3, 7, 11, 12, 13, 14, 15, 19, 23, 27, 28, 29, 30, 31, 35, 39, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 71, 75, 76, 77, 78, 79, 83, 87, 91, 92, 93, 94, 95, 99, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset: 1

François Marques, Sep 19 2020

Complementary sequence of A023717.

			18 is not in the sequence since it is 102_4 in base 4, but 19 is in the sequence since it is 103_4 in base 4.

François Marques, Table of n, a(n) for n = 1..10000

Cf. A196032 (at least one 0 in base 4).
Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), this sequence, A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).
Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

seq(`if`(numboccur(3, convert(n, base, 4))>0, n, NULL), n=0..100);

Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 4 ], 3 ]>0)& ]

isok(m) = #select(x->(x==3), digits(m, 4)) >= 1; \\ Michel Marcus, Sep 20 2020

from gmpy2 import digits
def A337250(n):
    def f(x):
        l = (s:=digits(x,4)).find('3')
        if l >= 0: s = s[:l]+'2'*(len(s)-l)
        return n+int(s,3)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

cp's OEIS Frontend

A052419 Numbers without 7 as a digit.

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A171397 Write n in base 10, but then read it as if it were written in base 11: if n = Sum_{i >= 0} d_i*10^i, with 0 <= d_i <= 9, then a(n) = Sum_{i >= 0} d_i*11^i.

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A037465 a(n) = Sum_{i=0..m} d(i)*6^i, where Sum_{i=0..m} d(i)*5^i is the base 5 representation of n.

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A052406 Numbers without 4 as a digit.

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A338090 Numbers having at least one 8 in their representation in base 9.

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A037474 a(n) = Sum{d(i)*8^i: i=0,1,...,m}, where Sum{d(i)*7^i: i=0,1,...,m} is the base 7 representation of n.

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A171397 Write n in base 10, but then read it as if it were written in base 11: if n = Sum_{i >= 0} d_i10^i, with 0 <= d_i <= 9, then a(n) = Sum_{i >= 0} d_i11^i.

A037465 a(n) = Sum_{i=0..m} d(i)6^i, where Sum_{i=0..m} d(i)5^i is the base 5 representation of n.

A037474 a(n) = Sum{d(i)8^i: i=0,1,...,m}, where Sum{d(i)7^i: i=0,1,...,m} is the base 7 representation of n.

A037477 a(n) = Sum{d(i)9^i: i=0,1,...,m}, where Sum{d(i)8^i: i=0,1,...,m} is the base 8 representation of n.