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 1-6 of 6 results.

A030086 Primes p whose digits do not appear in p^2.

Original entry on oeis.org

2, 3, 7, 17, 29, 47, 53, 59, 67, 79, 157, 173, 257, 307, 313, 349, 353, 359, 409, 449, 467, 547, 557, 577, 659, 673, 677, 739, 787, 853, 929, 1447, 1607, 1747, 2029, 2087, 2113, 2237, 3257, 3359, 3467, 3533, 3559, 3767, 3779, 4253, 4337, 4787, 5333, 5557, 5659
Offset: 1

Views

Author

Patrick De Geest, Dec 11 1999

Keywords

Comments

Primes of sequence A029783. - Michel Marcus, Jan 04 2015

Examples

			2 and 2^2 = 4 have no digits in common, hence 2 is in the sequence.

Links

Crossrefs

Cf. A029783 (numbers n whose digits are not present in n^2).
Cf. similar sequences listed in A253574.

Programs

  • Mathematica
    Select[Prime[Range[700]],Intersection[IntegerDigits[#],IntegerDigits[ #^2]] == {}&] (* Harvey P. Dale, Oct 02 2014 *)
  • PARI
    lista(nn) = {forprime (n=1, nn, if (#setintersect(Set(vecsort(digits(n^2))), Set(vecsort(digits(n)))) == 0, print1(n, ", ")); ); } \\ Michel Marcus, Jan 04 2015

Extensions

Offset changed from 0 to 1 from Vincenzo Librandi, Jan 04 2015

A030087 Primes such that digits of p do not appear in p^3.

Original entry on oeis.org

2, 3, 7, 43, 47, 53, 157, 223, 263, 487, 577, 587, 823, 4657, 5657, 6653, 7177, 8287, 9343, 26777, 36293, 46477, 58787, 72727, 75707, 176777, 363313, 530353, 566653, 959953, 1771787, 2525557, 2555353, 2626277, 3656363, 4414447, 7110707, 8448343, 20700077, 54475457, 71117177, 72722977, 135135113, 393321293, 457887457, 505053053, 672722627
Offset: 1

Views

Author

Patrick De Geest, Dec 11 1999

Keywords

Comments

Primes of sequence A029785. - Michel Marcus, Jan 04 2015

Examples

			2 and 2^3=8 have no digits in common, hence 2 is in the sequence.

Links

Crossrefs

Cf. A029785 (digits of n are not present in n^3), A030086 (similar, with p^2), A253574 (similar, with p^4).

Programs

  • Mathematica
    Select[Prime[Range[1500000]], Intersection[IntegerDigits[#], IntegerDigits[#^3]]=={} &] (* Vincenzo Librandi, Jan 04 2015 *)
  • PARI
    lista(nn) = {forprime (n=1, nn, if (#setintersect(Set(vecsort(digits(n^3))), Set(vecsort(digits(n)))) == 0, print1(n, ", ")); ); } \\ Michel Marcus, Jan 04 2015
  • Python
    from sympy import isprime
A030087_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**3)) == set() and isprime(n)]
# Chai Wah Wu, Jan 05 2015

Extensions

Changed offset from 0 to 1 and more terms from Vincenzo Librandi, Jan 04 2015
a(40)-a(47) from Chai Wah Wu, Jan 05 2015

A253576 Primes p such that digits of p do not appear in p^7.

Original entry on oeis.org

3, 7, 43, 7757, 31333
Offset: 1

Views

Author

Vincenzo Librandi, Jan 04 2015

Keywords

Comments

a(6) > 10^9. - Chai Wah Wu, Jan 05 2015

Examples

			3 and 3^7 = 2187 have no digits in common, hence 3 is in the sequence.

Crossrefs

Prime numbers in A281678.
Cf. similar sequences listed in A253574.

Programs

  • Mathematica
    Select[Prime[Range[1000000]], Intersection[IntegerDigits[#], IntegerDigits[#^7]]=={} &]
  • Python
    from sympy import isprime
A253576_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**7)) == set() and isprime(n)]
# Chai Wah Wu, Jan 05 2015

A253577 Primes p such that digits of p do not appear in p^8.

Original entry on oeis.org

3, 43, 59, 73, 233, 353
Offset: 1

Views

Author

Vincenzo Librandi, Jan 04 2015

Keywords

Comments

a(7) > 10^7.
Subsequence of A253606. a(7) > 10^9. - Chai Wah Wu, Jan 05 2015

Examples

			3 and 3^8 = 6561 have no digits in common, hence 3 is in the sequence.

Crossrefs

Cf. similar sequences listed in A253574.

Programs

  • Mathematica
    Select[Prime[Range[1000000]], Intersection[IntegerDigits[#], IntegerDigits[#^8]]=={} &]
  • Python
    from sympy import isprime
A253577_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**8)) == set() and isprime(n)]
# Chai Wah Wu, Jan 05 2015

A253575 Primes p such that digits of p do not appear in p^6.

Original entry on oeis.org

2, 3, 13, 44449
Offset: 1

Views

Author

Vincenzo Librandi, Jan 04 2015

Keywords

Comments

a(5) > 10^9. - Chai Wah Wu, Jan 05 2015

Examples

			2 and 2^6 = 64 have no digits in common, hence 2 is in the sequence.

Crossrefs

Primes in A281148.
Cf. similar sequences listed in A253574.

Programs

  • Maple
    select(t -> isprime(t) and convert(convert(t,base,10),set) intersect convert(convert(t^6,base,10),set) = {},
{2, seq(i,i=3..10^5,2)}); # Robert Israel, May 25 2025
  • Mathematica
    Select[Prime[Range[1000000]], Intersection[IntegerDigits[#], IntegerDigits[#^6]]=={} &]
  • Python
    from sympy import isprime
A253575_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**6)) == set() and isprime(n)]
# Chai Wah Wu, Jan 05 2015

A253578 Primes p such that digits of p do not appear in p^10.

Original entry on oeis.org

3, 877
Offset: 1

Views

Author

Vincenzo Librandi, Jan 05 2015

Keywords

Comments

a(3) > 10^7.
Numbers n < 10^7 such that digits of n are not present in n^10: 3, 9, 18, 877, 5757.
a(3) > 10^10. - Chai Wah Wu, Jan 15 2015

Examples

			3 and 3^10 = 59049 have no digits in common, hence 3 is in the sequence.

Crossrefs

Cf. similar sequences listed in A253574.

Programs

  • Mathematica
    Select[Prime[Range[1000000]], Intersection[IntegerDigits[#], IntegerDigits[#^10]]=={} &]
  • Python
    from sympy import isprime
A253578_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**10)) == set() and isprime(n)] # Chai Wah Wu, Jan 15 2015
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.