cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 21 results. Next

A038618 Primes not containing the digit '0'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 127, 131, 137, 139, 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
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Complement of A056709 with respect to primes (A000040). - Lekraj Beedassy, Jul 04 2010
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Links

Crossrefs

Cf. A010051, A168046, A384793, A384794.
Subsequence of A000040 (primes), A052382 (zeroless numbers) and A195943.
Primes having no digit d = 0..9 are this sequence, A038603, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.

Programs

  • Haskell
    a038618 n = a038618_list !! (n-1)
a038618_list = filter ((== 1) . a168046) a000040_list
-- Reinhard Zumkeller, Apr 07 2014, Sep 27 2011
  • Magma
    [ p: p in PrimesUpTo(300) | not 0 in Intseq(p) ];  // Bruno Berselli, Aug 08 2011
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 0] == 0 &] (* Vincenzo Librandi, Aug 09 2011 *)
  • PARI
    is(n)=if(isprime(n),n=vecsort(eval(Vec(Str(n))),,8);n[1]>0) \\ Charles R Greathouse IV, Aug 09 2011
  • PARI
    lista(nn) = forprime (p=2, nn, if (vecmin(digits(p)), print1(p, ", "))); \\ Michel Marcus, Apr 06 2016
  • PARI
    next_A038618(n)=until(vecmin(digits(n=nextprime(next_A052382(n)))),);n \\ Cf. OEIS Wiki page (LINKS) for other programs. - M. F. Hasler, Jan 12 2020
  • Python
    from sympy import primerange
def aupto(N): return [p for p in primerange(1, N+1) if '0' not in str(p)]
print(aupto(300)) # Michael S. Branicky, Mar 11 2022

Formula

Intersection of A052382 (zeroless numbers) and A000040 (primes); A168046(a(n))*A010051(a(n)) = 1. - Reinhard Zumkeller, Dec 01 2009
a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

A038603 Primes not containing the digit '1'.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 223, 227, 229, 233, 239, 257, 263, 269, 277, 283, 293, 307, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 409, 433, 439, 443, 449, 457, 463, 467, 479, 487, 499, 503, 509, 523, 547, 557
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Subsequence of A132080. - Reinhard Zumkeller, Aug 09 2007
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Links

Crossrefs

Intersection of A000040 (primes) and A052383 (numbers with no digit 1).
Primes having no digit d = 0..9 are A038618, this sequence, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.
Primes with other restrictions on digits: A106116, A156756.

Programs

  • Magma
    [ p: p in PrimesUpTo(600) | not 1 in Intseq(p) ];  // Bruno Berselli, Aug 08 2011
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 1] == 0 &] (* Vincenzo Librandi, Aug 09 2011 *)
  • PARI
    is(n)=if(isprime(n),n=vecsort(eval(Vec(Str(n))),,8);n[1]>1||(!n[1]&&n[2]>1)) \\ Charles R Greathouse IV, Aug 09 2011
  • PARI
    is(n)=!vecsearch(vecsort(digits(n)),1) && isprime(n) \\ Charles R Greathouse IV, Oct 03 2012
  • PARI
    next_A038603(n)=until((n=nextprime(n+1))==n=next_A052383(n-1),);n \\ Compute least a(k) > n. See A052383. - M. F. Hasler, Jan 14 2020
  • Python
    from sympy import nextprime
i=p=1
while i<=500:
    p = nextprime(p)
    if '1' not in str(p):
        print(str(i)+" "+str(p))
        i+=1
# Indranil Ghosh, Feb 07 2017, edited by M. F. Hasler, Jan 15 2020
# See the OEIS Wiki page for more efficient programs. - M. F. Hasler, Jan 14 2020

Formula

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

A038615 Primes not containing the digit '7'.

Original entry on oeis.org

2, 3, 5, 11, 13, 19, 23, 29, 31, 41, 43, 53, 59, 61, 83, 89, 101, 103, 109, 113, 131, 139, 149, 151, 163, 181, 191, 193, 199, 211, 223, 229, 233, 239, 241, 251, 263, 269, 281, 283, 293, 311, 313, 331, 349, 353, 359, 383, 389, 401, 409, 419, 421, 431, 433, 439
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Subsequence of primes of A052419. - Michel Marcus, Feb 22 2015
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Links

Crossrefs

Cf. A000040, A052419.
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, this sequence, A038616, and A038617, respectively.

Programs

  • Magma
    [ p: p in PrimesUpTo(500) | not 7 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 7] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
  • PARI
    lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 7), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015
  • PARI
    (A038615_upto(N)=select( is_A052419, primes([1,N])))(444) \\ i.e.: {is_A038615(n)=is_A052419(n)&&isprime(n)}; {is_A052419(n)=!setsearch(Set(digits(n)),7)}. - M. F. Hasler, Jan 11 2020

Formula

Intersection of A000040 (primes) and A052419 (numbers with no digit 7). - M. F. Hasler, Jan 11 2020
a(n) ~ n^(log 10/log 9) * log(n). - Charles R Greathouse IV, Aug 03 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038611 Primes not containing the digit '3'.

Original entry on oeis.org

2, 5, 7, 11, 17, 19, 29, 41, 47, 59, 61, 67, 71, 79, 89, 97, 101, 107, 109, 127, 149, 151, 157, 167, 179, 181, 191, 197, 199, 211, 227, 229, 241, 251, 257, 269, 271, 277, 281, 401, 409, 419, 421, 449, 457, 461, 467, 479, 487, 491, 499, 509, 521, 541, 547, 557
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Subsequence of primes of A052405. - Michel Marcus, Feb 22 2015
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Links

Crossrefs

Intersection of A000040 (primes) and A052405 (numbers with no digit 3).
Primes having no digit d = 0..9 are A038618, A038603, A038604, this sequence, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.

Programs

  • Magma
    [ p: p in PrimesUpTo(600) | not 3 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 3] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
  • PARI
    lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 3), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015
  • PARI
    ( {A038611_upto(N,M=1)=select( is_A052405, primes([M,N]))} )(350)
  • PARI
    next_A038611(n)={until((n=nextprime(n+1))==n=next_A052405(n-1),);n}
( {A038611_vec(n,M=2)=M--;vector(n,i,M=next_A038611(M))} )(20, 1000)
\\ Get 20 terms >= 1000. See also OEIS wiki page. - M. F. Hasler, Jan 14 2020
  • Python
    from sympy import isprime
i=j=1
while j<=5000:
    if isprime(i) and "3" not in str(i):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 07 2017

Formula

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038604 Primes not containing the digit '2'.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Subsequence of primes of A052404. - Michel Marcus, Feb 21 2015
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Links

Crossrefs

Cf. A000040, A052404.
Subsequence of A065091 (odd primes).
Primes having no digit d = 0..9 are A038618, A038603, this sequence, A038611, A038612, A038613, A038614, A038615, A038616, and A038617, respectively.

Programs

  • Magma
    [ p: p in PrimesUpTo(400) | not 2 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 2] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
  • PARI
    lista(nn, d=2) = {forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), d), print1(p, ", ")););} \\ Michel Marcus, Feb 21 2015
  • PARI
    select( {is_A038604(n)=is_A052404(n)&&isprime(n)}, [1..400]) \\ see Wiki for more
{next_A038604(n)=until((n==nextprime(n+1))==n=next_A052404(n-1),);n} \\ M. F. Hasler, Jan 12 2020
  • Python
    from sympy import isprime, nextprime
def is_A038604(n): return str(n).find('2')<0 and isprime(n)
def next_A038604(n): # get smallest term > n
    while True:
        n = nextprime(n); s = str(n); t = s.find('2')
        if t < 0: return n
        t = 10**(len(s)-1-t); n += t - n%t
def A038604_upto(stop=math.inf, start=3):
    while start < stop: yield start; start = next_A038604(start)
list(A038604_upto(400))
# M. F. Hasler, Jan 12 2020

Formula

Intersection of A000040 and A052404. - M. F. Hasler, Jan 11 2020
a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038612 Primes not containing the digit '4'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 293
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Subsequence of primes of A052406. - Michel Marcus, Feb 22 2015
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Links

Crossrefs

Intersection of A000040 (primes) and A052406 (numbers without digit 4).
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, this sequence, A038613, A038614, A038615, A038616, and A038617, respectively.

Programs

  • Magma
    [ p: p in PrimesUpTo(300) | not 4 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 4] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
  • PARI
    lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 4), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015
  • PARI
    ( {A038612_upto(N)=select( is_A052406, primes([1, N]))} )(444) \\ or better:
next_A038612(n)={until(isprime(n), n=next_A052406(nextprime(n+1)-1)); n}
( {A038612_vec(n,M=1)=M--;vector(n,i, n=next_A038612(if(i>1, n)))} )(20, 1000)
\\ (See the OEIS wiki page for more.) - M. F. Hasler, Jan 12 2020

Formula

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038614 Primes not containing the digit '6'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 271, 277, 281, 283, 293, 307, 311
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Subsequence of primes of A052414. - Michel Marcus, Feb 22 2015
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Links

Crossrefs

Intersection of A000040 (primes) and A052414 (numbers with no digit 6).
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, this sequence, A038615, A038616, and A038617, respectively.

Programs

  • Magma
    [ p: p in PrimesUpTo(400) | not 6 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
  • Maple
    no6:= proc(n) option remember;
  n mod 10 <> 6 and procname(floor(n/10))
end proc:
no6(0):= true:
select(no6 and isprime, [2,seq(i,i=3..1000,2)]); # Robert Israel, Mar 16 2017
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 6] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
  • PARI
    lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 6), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015
  • PARI
    select( {is_A038614(n)=is_A052414(n)&&isprime(n)}, [1..350]) \\ see A052414
(A038614_upto(n)=select( is_A038614, primes([1,n])))(350) \\ needs the above
next_A038614(n)={until(isprime(n), n=next_A052414(nextprime(n+1)-1));n}
(A038614_vec(n)=vector(n,i,n=next_A038614(if(i>1,n))))(66) \\ M. F. Hasler, Jan 12 2020

Formula

Intersection of A000040 and A052414. - M. F. Hasler, Jan 12 2020
a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038613 Primes not containing the digit '5'.

Original entry on oeis.org

2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 263, 269, 271, 277, 281, 283, 293, 307, 311
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Subsequence of primes of A052413. - Michel Marcus, Feb 22 2015
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Examples

			From _M. F. Hasler_, Jan 14 2020: (Start)
After a(85) = 499, the next prime without digit 5 is a(86) = 601.
After a(3734) = 49999, the next term is a(3735) = 60013.
After a(27273) = 499979, the next term is 600011.
After a(206276) = 4999999, the next term is 6000011. (End)

Links

Crossrefs

Intersection of A000040 (primes) and A052413 (numbers with no digit 5).
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, this sequence, A038614, A038615, A038616, and A038617, respectively.

Programs

  • Magma
    [ p: p in PrimesUpTo(400) | not 5 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 5] == 0 &] (* Vincenzo Librandi, Aug 08 2011 *)
  • PARI
    lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 5), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015
  • PARI
    (A038613_upto(n)=select( is_A052413, primes([1, n])))(350) \\ see A052413
next_A038613(n)={until(isprime(n), n=next_A052413(nextprime(n+1)-1)); n}
( {A038613_vec(n, M=1)=M--;vector(n, i, M=next_A038613(M))} )(20, 1000) \\ Compute n terms >= M. See also the OEIS wiki page. - M. F. Hasler, Jan 14 2020

Formula

a(n) ≍ n^(log 10/log 9) log n. - Charles R Greathouse IV, Aug 03 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A038616 Primes not containing the digit '8'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 293, 307
Offset: 1

Views

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Keywords

Comments

Subsequence of primes of A052421. - Michel Marcus, Feb 22 2015
Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Links

Crossrefs

Intersection of A000040 (primes) and A052421 (numbers with no 8).
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, A038615, this sequence, and A038617, respectively.

Programs

  • Magma
    [ p: p in PrimesUpTo(400) | not 8 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011
  • Mathematica
    Select[Prime[Range[70]], DigitCount[#, 10, 8] == 0 &] (* Harvey P. Dale, Jan 24 2011 *)
  • PARI
    lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 8), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015
  • PARI
    next_A038616(n)=until((n=nextprime(n+1))==(n=next_A052421(n-1)), ); n \\ M. F. Hasler, Jan 14 2020

Formula

a(n) ~ n^(log 10/log 9) * log(n). - Charles R Greathouse IV, Aug 03 2023

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 07 2011

A036964 Primes with digits (0,...,8) taken as base 9 and converted to base 10.

Original entry on oeis.org

2, 3, 5, 7, 10, 12, 16, 21, 28, 34, 37, 39, 43, 48, 55, 61, 64, 66, 75, 82, 84, 88, 93, 106, 109, 115, 127, 133, 138, 142, 147, 154, 172, 183, 187, 192, 199, 208, 214, 219, 226, 232, 235, 237, 250, 253, 255, 259, 271, 277, 286, 291, 304, 309, 318, 325, 343, 352
Offset: 1

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Examples

			a(n)=343 -> is 421{9} -> 421{10} is prime.

Crossrefs

Cf. A038617, A036952-A036963.

Extensions

Offset 1 from Michel Marcus, Oct 10 2019
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