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 1-5 of 5 results.

A134966 Primes that use all of the prime digits 2,3,5,7 exactly once.

Original entry on oeis.org

2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523
Offset: 1

Views

Author

Lekraj Beedassy, Feb 04 2008

Keywords

Comments

Permutations of the four prime digits 2, 3, 5, 7 that are primes. - Lekraj Beedassy, May 12 2009

Crossrefs

Cf. A108419, A124674, A177275.

Programs

  • Mathematica
    Select[FromDigits/@Permutations[{2,3,5,7}],PrimeQ] (* Harvey P. Dale, Jul 04 2013 *)

A124673 Numbers with distinct prime digits.

Original entry on oeis.org

2, 3, 5, 7, 23, 25, 27, 32, 35, 37, 52, 53, 57, 72, 73, 75, 235, 237, 253, 257, 273, 275, 325, 327, 352, 357, 372, 375, 523, 527, 532, 537, 572, 573, 723, 725, 732, 735, 752, 753, 2357, 2375, 2537, 2573, 2735, 2753, 3257, 3275, 3527, 3572, 3725, 3752, 5237
Offset: 1

Views

Author

Tanya Khovanova, Dec 24 2006

Keywords

Links

Crossrefs

Cf. A019546, A124674.

Programs

  • Mathematica
    Select[Range[10000], Length[IntegerDigits[ # ]] == Length[Union[IntegerDigits[ # ]]] && Complement[IntegerDigits[ # ], {2, 3, 5, 7}] == {} &]
Rest[FromDigits/@Flatten[Permutations/@Subsets[{2,3,5,7}],1]]//Sort (* Harvey P. Dale, Jun 02 2024 *)

A141521 Primes with a prime number of digits, all of which are distinct primes.

Original entry on oeis.org

23, 37, 53, 73, 257, 523
Offset: 1

Views

Author

Lekraj Beedassy, Aug 11 2008

Keywords

Crossrefs

Cf. A124888, A124674.

Programs

  • Mathematica
    Sort[Select[FromDigits/@Flatten[Permutations/@Subsets[{2,3,5,7},{2,3}],1],PrimeQ]] (* Harvey P. Dale, Jul 08 2014 *)

A323391 Primes containing nonprime digits (from 1 to 9) in their decimal expansion and whose digits are distinct, i.e., consisting of only digits 1, 4, 6, 8, 9.

Original entry on oeis.org

19, 41, 61, 89, 149, 419, 461, 491, 619, 641, 691, 941, 1489, 4691, 4861, 6481, 6491, 6841, 8419, 8461, 8641, 8941, 9461, 14869, 46819, 48619, 49681, 64189, 64891, 68491, 69481, 81649, 84691, 84961, 86491, 98641
Offset: 1

Views

Author

Bernard Schott, Jan 13 2019

Keywords

Comments

There are only 36 terms in this sequence, which is a finite subsequence of A152313.
Two particular examples:
6481 is also the smallest prime formed from the concatenation of two consecutive squares.
81649 is the only prime containing all the nonprime positive digits such that every string of two consecutive digits is a square.

Examples

			14869 is the smallest prime that contains all the nonprime positive digits; 98641 is the largest one.

Links

  • Chris K. Caldwell and G. L. Honaker, Jr., 81649, Prime Curios!

Crossrefs

Subsequence of A152313. Subsequence of A029743. Subsequence of A155024 (with distinct nonprime digits but with 0) and of A034844.
Cf. A029743 (with distinct digits), A124674 (with distinct prime digits), A155045 (with distinct odd digits), A323387 (with distinct square digits), A323578 (with distinct digits for which parity of digits alternates).

Programs

  • Mathematica
    Select[Union@ Flatten@ Map[FromDigits /@ Permutations@ # &, Rest@ Subsets@ {1, 4, 6, 8, 9}], PrimeQ] (* Michael De Vlieger, Jan 19 2019 *)
  • PARI
    isok(p) = isprime(p) && (d=digits(p)) && vecmin(d) && (#Set(d) == #d) && (#select(x->isprime(x), d) == 0); \\ Michel Marcus, Jan 14 2019

A323579 Primes formed by using the four terminal digits of multidigit primes and whose digits are distinct, i.e., consisting of only digits 1, 3, 7, 9.

Original entry on oeis.org

3, 7, 13, 17, 19, 31, 37, 71, 73, 79, 97, 137, 139, 173, 179, 193, 197, 317, 379, 397, 719, 739, 937, 971, 1973, 3719, 3917, 7193, 9137, 9173, 9371
Offset: 1

Views

Author

Bernard Schott, Jan 24 2019

Keywords

Comments

There are only 31 terms in this sequence, which is a finite subsequence of A091633 and of A155045.
719 is also the third factorial prime belonging to A055490.

Examples

			1973 and 9371 are respectively the smallest and the largest primes formed with the four digits that can end multidigit primes.

Links

  • Chris K. Caldwell and G. L. Honaker, Jr., 9371, Prime Curios!

Crossrefs

Subsequence of A091633 and hence of A030096.
Cf. A029743 (with distinct digits), A124674 (with distinct prime digits), A155024 (with distinct nonprime digits but with 0), A155045 (with distinct odd digits), A323387 (with distinct square digits), A323391 (with distinct nonprime digits), A323578 (with distinct digits for which parity of digits alternates).

Programs

  • Mathematica
    With[{w = Select[Range@ 10, GCD[#, 10] == 1 &]}, Select[FromDigits /@ Permutations[w, Length@ w], PrimeQ]] (* Michael De Vlieger, Feb 03 2019 *)
Select[FromDigits/@Flatten[Permutations/@Subsets[{1,3,7,9}],1],PrimeQ]//Union (* Harvey P. Dale, Apr 20 2025 *)
Showing 1-5 of 5 results.

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

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