A011760 -id:A011760 - cp's OEIS frontend

A052406 Numbers without 4 as a digit.

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

A085265 Numbers that can be written as sum of a positive squarefree number and a positive square.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 1

Reinhard Zumkeller, Jun 23 2003

Subsequence of A011760; A085263(a(n)) > 0.
Conjecture: a(n) = n + 2 for n > 11. That is, only 1 and 13 are missing. - Charles R Greathouse IV, Aug 21 2011
Estermann proves that only finitely many positive integers are missing from this sequence. (Probably only 1 and 13.) - Charles R Greathouse IV, Jul 01 2016

Theodor Estermann, Einige Sätze über quadratfreie Zahlen, Mathematische Annalen 105:1 (1931), pp. 653-662.
Eric Weisstein's World of Mathematics, Square Number
Eric Weisstein's World of Mathematics, Squarefree

is(n)=forstep(k=sqrtint(n-1), 1, -1, if(issquarefree(n-k^2), return(1))); 0 \\ Charles R Greathouse IV, Mar 12 2012

A113763 Non-multiples of 13, or numbers not divisible by 13.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

Zak Seidov, Jan 18 2006

Cf. A011760 (Elevator buttons in U.S.A).
Cf. A023806 (all digits in base 12 are different).
Complement of A008595. - Reinhard Zumkeller, Apr 26 2011

Eric Weisstein's World of Mathematics, Triskaidekaphobia
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Cf. A011760, A023806.

Table[n+Quotient[2n-1, 24], {n, 1, 85}];(* or *)Table[n+Floor[(2n-1)/24], {n, 1, 85}]

a(n)=(26*n-1)\24 \\ Charles R Greathouse IV, Jun 08 2015

[i for i in range(80) if not i%13] # Zerinvary Lajos, Apr 21 2009

a(n) = n+floor((2n-1)/24) = n+quotient(2n-1, 24)

A076805 Triskaidekaphobic or 13-free primes: primes that do not contain the number 13.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 127, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307

Offset: 1

Cino Hilliard, Nov 18 2002

			The PARI program will mask out a sequence containing k or mask in a sequence containing k. The program is limited to primes < 400000000.
The PARI program will generate the following for input as shown: kprimes(2,100,7,0) = 2 3 5 11 13 19 23 29 31 41 43 53 59 61 83 89; kprimes(2,1000,13,1) = 13 113 131 137 139 313 613; kprimes(300000,4000000,314159,1) = 314159 3314159 5314159

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triskaidekaphobia
Wikipedia, Triskaidekaphobia

A generalization of the examples A038603, A038615 etc. for k = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 by Vasiliy Danilov.
Cf. A038615 A038603.
Complement of A166573 with respect to A000040; cf. A011760

import Data.List (isInfixOf)
a076805 n = a076805_list !! (n-1)
a076805_list = filter (not . ("13" `isInfixOf`) . show) a000040_list
-- Reinhard Zumkeller, Nov 09 2011

Select[Prime[Range[90]],!MemberQ[Partition[IntegerDigits[#],2,1],{1,3}]&] (* Harvey P. Dale, Mar 25 2012 *)
Select[Prime[Range[100]],SequenceCount[IntegerDigits[#],{1,3}]==0&] (* Harvey P. Dale, Aug 11 2023 *)

/* k primes - kprimes.gp. Primes containing or not containing digit k=1,2,3...9,10,11... PARI does not have a good string manipulation capability. This program circumvents that by using the % modulo and floor operators. Also commented out is a log implementation which is slower than string apps. The program either masks out prime numbers k or masks them in.*/

log10(z) = if(z>0,floor(log(z)/log(10))+1,1);\\integer function for log(z) base 10 + 1
{ kprimes(n1,n2,k,t) = \\n1,n2=range,k=mask,t=0 mask out t=1 mask in
ct=0; pct=0; forprime(p=n1,n2,x=p; f=0;\\x=temp variable to diminish p
ln = length(Str(p));\\get length of the prime p using strings
lk = length(Str(k));\\get length of mask integer k using strings
ln = log10(p);\\get length of the prime p using logs
lk = log10(k);\\get length of mask integer k using strings
r = 10^lk; \\set the remainder length = length of k
for(j=1,ln-lk+1, \\permute through the digits
d = x % r;\\get lk digits
if(d==k,f=1; break);\\break for loop if match and set flag
x = floor(x/10);\\diminish x for next test for k
); if(f==t,print1(p" "); ct+=1);\\if no k string of digits,print
); print(); print(ct); }

hasNo13(n)=n=digits(n); for(i=2,#n, if(n[i]==3&&n[i-1]==1, return(0))); 1
select(hasNo13, primes(10^4)) \\ Charles R Greathouse IV, Dec 02 2013

is_A076805(n,t=13)=!until(t>n\=10,t==n%100&&return) \\ M. F. Hasler, Dec 02 2013

a(n) >> n^1.0044, where the exponent is log(r)/log(10) with r the larger root of x^2 - 10x + 1. [Charles R Greathouse IV, Nov 09 2011]

kfreep(n, k) = true if for primes p over the range n and integer k, p mod 10^(floor(log_10(k))+1) <> k for p = p/10 mod 10^(floor(log_10(k))+1) <> k over the range floor(log_10(k))+1. This is a mathematical definition of the recurrence. In practice it is convenient to use string operations. E.g., If Not Instr(Str(p), Str(k)) then true or k is not a substring of p so list p.

Original PARI code restored by M. F. Hasler, Dec 02 2013

cp's OEIS Frontend

A052406 Numbers without 4 as a digit.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

PARI

Python

Python

sh

Formula

Extensions

A085265 Numbers that can be written as sum of a positive squarefree number and a positive square.

Views

Author

Keywords

Comments

Links

Programs

PARI

A113763 Non-multiples of 13, or numbers not divisible by 13.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Formula

A076805 Triskaidekaphobic or 13-free primes: primes that do not contain the number 13.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

PARI

PARI

PARI

Formula

Extensions