A020452 -id:A020452 - cp's OEIS frontend

A260267 Primes having only {1, 2, 4} as digits.

2, 11, 41, 211, 241, 421, 2111, 2141, 2221, 2411, 2441, 4111, 4211, 4241, 4421, 4441, 11411, 12211, 12241, 12421, 14221, 14411, 21121, 21211, 21221, 22111, 22441, 24121, 24421, 41141, 41221, 41411, 42221, 44111, 44221, 111121, 111211, 112111, 112121, 112241

Offset: 1

Vincenzo Librandi, Jul 23 2015

A020450 and A020452 are subsequences.

All terms but the first one end with a digit "1". - M. F. Hasler, Jul 26 2015

Cf. similar sequences listed in A260266.

Cf. A020450, A020452.

[p: p in PrimesUpTo(4*10^5) | Set(Intseq(p)) subset [1, 4, 2]];

Select[Prime[Range[3 10^4]], Complement[IntegerDigits[#], {1, 4, 2}]=={} &]

A260267(n=50,show=0)={for(d=1,1e9,my(t,u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,[0,if(iM. F. Hasler, Jul 25 2015

A260271 Primes having only {1, 4, 9} as digits.

Original entry on oeis.org

11, 19, 41, 149, 191, 199, 419, 449, 491, 499, 911, 919, 941, 991, 1499, 1949, 1999, 4111, 4441, 4919, 4999, 9199, 9419, 9491, 9941, 9949, 11119, 11149, 11411, 11491, 11941, 14149, 14411, 14419, 14449, 19141, 19441, 19919, 19949, 19991, 41141, 41149, 41411

Offset: 1

Vincenzo Librandi, Jul 23 2015

A020452, A020457 and A020466 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. similar sequences listed in A260266.

Cf. A020452, A020457, A020466.

[p: p in PrimesUpTo(5*10^4) | Set(Intseq(p)) subset [1, 4, 9]];

Select[Prime[Range[5 10^3]], Complement[IntegerDigits[#], {1, 4, 9}]=={} &]

A260266 Primes having only {0, 1, 4} as digits.

Original entry on oeis.org

11, 41, 101, 401, 4001, 4111, 4441, 10111, 10141, 11411, 14011, 14401, 14411, 40111, 41011, 41141, 41411, 44041, 44101, 44111, 100411, 101111, 101141, 101411, 110441, 114001, 114041, 140111, 140401, 140411, 141041, 141101, 400441, 401101, 401411, 404011

Offset: 1

Vincenzo Librandi, Jul 22 2015

A020449 and A020452 are subsequences.

All terms end with a digit "1". - M. F. Hasler, Jul 26 2015

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries for primes with digits in a given set

Primes that contain only digits among {1,4,k}: this sequence (k=0), A260267 (k=2), A199341 (k=3), A260268 (k=5), A260269 (k=6), A079651 (k=7), A260270 (k=8), A260271 (k=9).
Cf. A020449, A020452.
Cf. A020450 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349.

[p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [1, 4, 0]];

Select[Prime[Range[4 10^4]], Complement[IntegerDigits[#], {1, 4, 0}]=={} &]

A260266(n=50,show=0)={for(d=1,1e9,my(t,u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,[i==1||i==d,1+(iM. F. Hasler, Jul 25 2015

A199341 Primes having only {1, 3, 4} as digits.

Original entry on oeis.org

3, 11, 13, 31, 41, 43, 113, 131, 311, 313, 331, 431, 433, 443, 1433, 3313, 3331, 3343, 3413, 3433, 4111, 4133, 4441, 11113, 11131, 11311, 11411, 11443, 13313, 13331, 13411, 13441, 14143, 14341, 14411, 14431, 31333, 33113, 33311, 33331, 33343, 33413, 34141, 34313

Offset: 1

M. F. Hasler, Nov 05 2011

A020451, A020452 and A020461 are subsequences. - Vincenzo Librandi, Jul 26 2015

Robert Israel, Table of n, a(n) for n = 1..10000
Andrew Granville, Missing digits, and good approximations, arXiv:2308.03126 [math.NT], 2023. See p. 4.

Cf. A020449 - A020472, A199325 - A199329.

Cf. similar sequences listed in A199340.

[p: p in PrimesUpTo(10^5) | Set(Intseq(p)) subset [3, 4, 1]]; // Vincenzo Librandi, Jul 26 2015

Dmax:= 5: # to get all terms < 10^Dmax
Cd:= {1,3,4}:
C:= Cd:
for d from 2 to Dmax do
  Cd:= map(t -> (10*t+1,10*t+3,10*t+4),Cd);
  C:= C union Cd;
od:
sort(convert(select(isprime,C),list)); # Robert Israel, Jul 26 2015

Select[Prime[Range[4 10^3]], Complement[IntegerDigits[#], {3, 4, 1}]=={} &] (* Vincenzo Librandi, Jul 26 2015 *)

a(n, list=0, L=[1, 3, 4], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal & !isprime(A004086(t)) & next; list & print1(t", "); n--||return(t)))}

A032822 Numbers whose set of base-10 digits is {1,4}.

Original entry on oeis.org

1, 4, 11, 14, 41, 44, 111, 114, 141, 144, 411, 414, 441, 444, 1111, 1114, 1141, 1144, 1411, 1414, 1441, 1444, 4111, 4114, 4141, 4144, 4411, 4414, 4441, 4444, 11111, 11114, 11141, 11144, 11411, 11414, 11441, 11444, 14111, 14114

Offset: 1

Clark Kimberling

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for 10-automatic sequences.

Cf. A020452 (primes).

[n: n in [1..15000] | Set(IntegerToSequence(n, 10)) subset {1, 4}]; // Vincenzo Librandi, May 28 2012

Flatten[Table[FromDigits[#,10]&/@Tuples[{1,4},n],{n,5}]] (* Vincenzo Librandi, May 28 2012 *)

a[1]:1$ a[2]:4$ a[n]:= if oddp(n) then 10*a[floor(n/2)]+1 else 10*a[floor((n-1)/2)]+4$ makelist(a[n],n,1,40); /* Bruno Berselli, May 28 2012 */

def a(n): return int(bin(n+1)[3:].replace('1', '4').replace('0', '1'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 13 2021

def A032822(n): return 3*int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1)//9 # Chai Wah Wu, Jun 28 2025

a(1)=1, a(2)=4; a(n) = 10*a(floor(n/2))+1 for n odd, otherwise a(n) = 10*a(floor((n-1)/2))+4. - Bruno Berselli, May 28 2012

A260268 Primes having only {1, 4, 5} as digits.

Original entry on oeis.org

5, 11, 41, 151, 541, 1151, 1451, 1511, 4111, 4441, 4451, 5441, 11411, 11551, 14411, 14551, 15451, 15511, 15541, 15551, 41141, 41411, 44111, 45541, 51151, 51511, 51551, 54151, 54541, 55411, 55441, 55511, 55541, 114451, 115151, 141511, 141551, 144451, 144511

Offset: 1

Vincenzo Librandi, Jul 23 2015

A020452 and A020453 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. similar sequences listed in A260266.

Cf. A020452, A020453.

[p: p in PrimesUpTo(4*10^5) | Set(Intseq(p)) subset [1, 4, 5]];

Select[Prime[Range[3 10^4]], Complement[IntegerDigits[#], {1, 4, 5}]=={} &]

A260269 Primes having only {1, 4, 6} as digits.

Original entry on oeis.org

11, 41, 61, 461, 641, 661, 4111, 4441, 6661, 11161, 11411, 14411, 14461, 16111, 16141, 16411, 16661, 41141, 41161, 41411, 41611, 41641, 44111, 44641, 46141, 46411, 46441, 61141, 61441, 64661, 66161, 111611, 111641, 114161, 114641, 114661, 116141, 116411

Offset: 1

Vincenzo Librandi, Jul 23 2015

A020452 and A020454 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. similar sequences listed in A260266.

Cf. A020452, A020454.

[p: p in PrimesUpTo(4*10^5) | Set(Intseq(p)) subset [1, 4, 6]];

Select[Prime[Range[3 10^4]], Complement[IntegerDigits[#], {1, 4, 6}]=={} &]

A260270 Primes having only {1, 4, 8} as digits.

Original entry on oeis.org

11, 41, 181, 811, 881, 1181, 1481, 1811, 4111, 4441, 4481, 8111, 11411, 14411, 18181, 18481, 41141, 41411, 44111, 48481, 81181, 84181, 84481, 84811, 88411, 88811, 118411, 141181, 141481, 141811, 144481, 148411, 181141, 184111, 184181, 184441, 411841, 418181

Offset: 1

Vincenzo Librandi, Jul 23 2015

A020452 and A020456 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. similar sequences listed in A260266.

Cf. A020452, A020456.

[p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [1, 4, 8]];

Select[Prime[Range[4 10^4]], Complement[IntegerDigits[#], {1, 4, 8}]=={} &]
Table[Select[10#+1&/@(FromDigits/@Tuples[{1,4,8},n]),PrimeQ],{n,5}]// Flatten (* Harvey P. Dale, Jun 08 2019 *)

A036304 Composite numbers whose prime factors contain no digits other than 1 and 4.

Original entry on oeis.org

121, 451, 1331, 1681, 4961, 14641, 18491, 45221, 48851, 54571, 68921, 125521, 158521, 161051, 168551, 182081, 203401, 452551, 455521, 467851, 485221, 497431, 537361, 590851, 600281, 758131, 1380731, 1686781, 1697851, 1743731, 1771561

Offset: 1

Patrick De Geest, Dec 15 1998

All terms are a product of at least two terms of A020452. - David A. Corneth, Oct 09 2020

			The composite 4961 = 11^2 * 41 is in the sequence as the digits of its prime factors are either 1 or 4. - _David A. Corneth_, Oct 17 2020

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Alois P. Heinz)
Index entries for sequences related to prime factors.

Cf. A020452, A036302-A036325.

Sum_{n>=1} 1/a(n) = Product_{p in A020452} (p/(p - 1)) - Sum_{p in A020452} 1/p - 1 = 0.0122909749... . - Amiram Eldar, May 18 2022

A036931 Smallest n-digit prime containing only digits 1 and 4, or 0 if no such prime exists.

Original entry on oeis.org

0, 11, 0, 4111, 11411, 0, 1114111, 11111141, 0, 1111111411, 11111141411, 0, 1111111111441, 11111111111411, 0, 1111111111114441, 11111111111414411, 0, 1111111111111111111, 11111111111111414441, 0, 1111111111111111144141

Offset: 1

Patrick De Geest, Jan 04 1999

For any positive integer k, a(3k) = 0 as any 3k-digit number containing only digits 1 or 4 or both has a digit-sum divisible by 3 and thus the number is divisible by 3. - Rick L. Shepherd, Feb 08 2004

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Cf. A020452, A036304, A036229.

Cf. A004022 (repunit primes), A004023.

Flatten[Table[Select[FromDigits/@Tuples[{1, 4}, n], PrimeQ, 1], {n, 25}]/.{}->{0}] (* Jinyuan Wang, Mar 09 2020 *)

a(3k) = 0 and a(A004023(k)) = (10^A004023(k) - 1)/9 = A004022(k) for all positive integers k. - Rick L. Shepherd, Feb 08 2004

More terms from Rick L. Shepherd, Feb 08 2004

cp's OEIS Frontend

A260267 Primes having only {1, 2, 4} as digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A260271 Primes having only {1, 4, 9} as digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

A260266 Primes having only {0, 1, 4} as digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A199341 Primes having only {1, 3, 4} as digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

A032822 Numbers whose set of base-10 digits is {1,4}.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Maxima

Python

Python

Formula

A260268 Primes having only {1, 4, 5} as digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

A260269 Primes having only {1, 4, 6} as digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

A260270 Primes having only {1, 4, 8} as digits.

Views