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 1-9 of 9 results.

A057877 a(n) = smallest n-digit prime in A057876.

Original entry on oeis.org

23, 113, 1531, 12239, 111317, 1111219, 11119291, 111111197, 1111113173, 11111133017, 111111189919, 1111111411337, 11111111161177, 111111111263311, 1111111111149119, 11111111111179913, 111111111111118771, 1111111111111751371, 11111111111111111131, 111111111111113129773, 1111111111111111337111
Offset: 2

Views

Author

Patrick De Geest, Oct 15 2000

Keywords

Examples

			1531 gives primes 53, 131 and 151 after dropping digits 1, 5 and 3.

Crossrefs

Cf. A057876, A057877, A057878, A057879, A057880, A057881, A057882, A057883, A051362, A034302, A034303, A034304, A034305.

Programs

  • Maple
    filter:= proc(n) local L,d,Lp;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  for d in convert(L,set) do
    Lp:= subs(d=NULL,L);
    if Lp=[] or Lp[-1] = 0 then return false fi;
    if not isprime(add(Lp[i]*10^(i-1),i=1..nops(Lp))) then return false fi;
  od;
  true
end proc:
Res:= NULL:
for t from 1 to 21 do
  for x from (10^(t+1)-1)/9 by 2 do
    if filter(x) then Res:= Res, x; break fi
  od
od:
Res; # Robert Israel, Jul 13 2018
  • Mathematica
    Do[k = (10^n - 1)/9; While[d = IntegerDigits[k]; !PrimeQ[k] || !PrimeQ[ FromDigits[ DeleteCases[d, 0]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 1]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 2]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 3]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 4]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 5]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 6]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 7]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 8]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 9]]], k++ ]; Print[k], {n, 2, 19}]

Extensions

Extended by Robert G. Wilson v, Dec 17 2002
More terms from Robert Israel, Jul 13 2018

A057883 Smallest possible prime with at least n (from 2 to 10) distinct digits that remains prime (leading zeros not allowed) when all occurrences of its digits d are deleted.

Original entry on oeis.org

23, 137, 6173, 37019, 5600239, 476710937, 8192454631, 1645957688093, 78456580281239
Offset: 2

Views

Author

Patrick De Geest, Oct 15 2000

Keywords

Examples

			5600239 is a solution for at least 6 digits because 56239, 560039, 560029, 600239, 500239 and 560023 are all primes.

Links

Crossrefs

Cf. A057876-A057882, A051362, A034302-A034305.

Extensions

More terms from Giovanni Resta, Feb 15 2006

A108389 Transmutable primes with four distinct digits.

Original entry on oeis.org

133999337137, 139779933779, 173139331177, 173399913979, 177793993177, 179993739971, 391331737931, 771319973999, 917377131371, 933971311913, 997331911711, 1191777377177, 9311933973733, 9979333919939, 19979113377173, 31997131171111, 37137197179931, 37337319113911
Offset: 1

Views

Author

Rick L. Shepherd, Jun 02 2005

Keywords

Comments

This sequence is a subsequence of A108386 and of A108388. See the latter for the definition of transmutable primes and many more comments. Are any terms here doubly-transmutable also; i.e., terms of A108387? Palindromic too? Terms also of some other sequences cross-referenced below? a(7)=771319973999 is also a reversible prime (emirp). a(12)=9311933973733 also has the property that simultaneously removing all its 1's (93933973733), all its 3s (9119977) and all its 9s (3113373733) result in primes (but removing all 7s gives 93119339333=43*47*59*83*97^2, so a(12) is not also a term of A057876). Any additional terms have 14 or more digits.

Examples

			a(0)=133999337137 is the smallest transmutable prime with four distinct digits (1,3,7,9):
exchanging all 1's and 3's: 133999337137 ==> 311999117317 (prime),
exchanging all 1's and 7's: 133999337137 ==> 733999331731 (prime),
exchanging all 1's and 9's: 133999337137 ==> 933111337937 (prime),
exchanging all 3's and 7's: 133999337137 ==> 177999773173 (prime),
exchanging all 3's and 9's: 133999337137 ==> 199333997197 (prime) and
exchanging all 7's and 9's: 133999337137 ==> 133777339139 (prime).
No smaller prime with four distinct digits transmutes into six other primes.

Links

Crossrefs

Cf. A108386 (Primes p such that p's set of distinct digits is {1, 3, 7, 9}), A108388 (transmutable primes), A083983 (transmutable primes with two distinct digits), A108387 (doubly-transmutable primes), A006567 (reversible primes), A002385 (palindromic primes), A068652 (every cyclic permutation is prime), A107845 (transposable-digit primes), A003459 (absolute primes), A057876 (droppable-digit primes).

Extensions

a(14) and beyond from Michael S. Branicky, Dec 15 2023

A057880 Primes with 4 distinct digits that remain prime (no leading zeros allowed) after deleting all occurrences of its digits d.

Original entry on oeis.org

6173, 12239, 16673, 19531, 19973, 21613, 22397, 22937, 34613, 36137, 47933, 51193, 54493, 56519, 56531, 56591, 69491, 69497, 72937, 76873, 93497, 96419, 96479, 96497, 98837, 112939, 118213, 131779, 143419, 144497, 159319, 163337
Offset: 1

Views

Author

Patrick De Geest, Oct 15 2000

Keywords

Links

Crossrefs

Cf. A057876-A057883, A051362, A034302-A034305.

Programs

  • Maple
    filter:= proc(L) local d,Lp,i;
      if L[-1]=0 then return false fi;
      if not isprime(add(L[i]*10^(i-1),i=1..nops(L))) then return false fi;
      for d in convert(L,set) do
        Lp:= remove(`=`,L,d);
        if Lp[-1] = 0 or not isprime(add(Lp[i]*10^(i-1),i=1..nops(Lp))) then return false fi;
      od;
      true
end proc:
getCands:= proc(n, m) option remember;
   if m = 1 then return [seq([d$n], d=0..9)] fi;
   if n < m then return [] fi;
   [seq(seq([i,op(L)],i= {$0..9} minus convert(L,set)),L = procname(n-1,m-1)),
    seq(seq([i,op(L)],i=convert(L,set)),L = procname(n-1,m))]
end proc:
[seq(op(sort(map(t->add(t[i]*10^(i-1),i=1..nops(t)),select(filter,getCands(d,4))))),d=4..6)]; # Robert Israel, Jan 19 2017
  • Mathematica
    p4dQ[n_]:=Module[{idn=IntegerDigits[n]},Count[idn,0]==0 && Count[ DigitCount[ n],0]==6&&AllTrue[FromDigits/@Table[DeleteCases[idn,k],{k,Union[idn]}],PrimeQ]]; Select[Prime[Range[ 15000]],p4dQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 30 2017 *)

Extensions

Offset changed by Robert Israel, Jan 19 2017

A057882 Primes with 6 distinct digits that remain prime (no leading zeros allowed) after deleting all occurrences of its digits d.

Original entry on oeis.org

5600239, 21066319, 42209639, 63019679, 82190131, 95422517, 113420491, 114248737, 130194791, 132863191, 135160339, 137697019, 145136591, 145611439, 146414839, 153160517, 159136291, 181680713, 186601339, 186609331, 190714133
Offset: 1

Views

Author

Patrick De Geest, Oct 15 2000

Keywords

Crossrefs

Cf. A057876-A057883, A051362, A034302-A034305.

Extensions

Offset changed by Andrew Howroyd, Aug 14 2024

A057878 Primes with 2 distinct digits that remain prime (no leading zeros allowed) after deleting all occurrences of its digits d.

Original entry on oeis.org

23, 37, 53, 73, 113, 131, 151, 211, 311, 11111111111111111131, 11111111111111117111, 11111111111131111111, 11111111131111111111, 111111111111111111111113, 111111111111111112111111, 111111111111111121111111, 111111111112111111111111, 111111115111111111111111
Offset: 1

Views

Author

Patrick De Geest, Oct 15 2000

Keywords

Comments

Digits 0, 4, 6, 8, and 9 can never occur; digits 2, 3, 5, 7 can occur at most once in a term; every other digit is a 1. - Sean A. Irvine, Jul 11 2022

Crossrefs

Cf. A057876-A057883, A004022, A004023, A051362, A034302-A034305.

Extensions

More terms from Sean A. Irvine, Jul 11 2022

A057879 Primes with 3 distinct digits that remain prime (no leading zeros allowed) after deleting all occurrences of any one of its distinct digits.

Original entry on oeis.org

137, 173, 179, 197, 317, 431, 617, 719, 1531, 1831, 1997, 2113, 2131, 2237, 2273, 2297, 2311, 2797, 3137, 3371, 4337, 4373, 4733, 4919, 7297, 7331, 7573, 7873, 8191, 8311, 8831, 8837, 33413, 33713, 34313, 37313, 41117, 41999, 44417, 49199, 73331
Offset: 1

Views

Author

Patrick De Geest, Oct 15 2000

Keywords

Comments

Numbers in A057876 with exactly 3 distinct digits.

Crossrefs

Intersection of A057876 and A235155.
Cf. A057876-A057883, A051362, A034302-A034305.

Extensions

Offset changed by Andrew Howroyd, Aug 14 2024

A057881 Primes with 5 distinct digits that remain prime (no leading zeros allowed) after deleting all occurrences of its digits d.

Original entry on oeis.org

37019, 159013, 198013, 210139, 223697, 226397, 236297, 1305593, 1388693, 1393697, 1900937, 1912831, 2370673, 2796337, 2882093, 2930773, 3200191, 3202139, 3346199, 3442693, 3463199, 3463619, 3746399, 3769133, 4234039
Offset: 1

Views

Author

Patrick De Geest, Oct 15 2000

Keywords

Comments

Numbers in A057876 with exactly 5 distinct digits.

Crossrefs

Intersection of A057876 and A235157.
Cf. A057876-A057883, A051362, A034302-A034305.

Extensions

Offset changed by Andrew Howroyd, Aug 14 2024

A347200 Primes p with the following property: let d_1, d_2, ... be the distinct digits occurring in the decimal expansion of p. Then for each d_i, dropping all the digits d_i from p produces a prime number, and for each digit pair (d_i, d_j), dropping all the digits d_i and all the digits d_j from p also produces a prime number. Leading 0's are not allowed.

Original entry on oeis.org

1531, 2113, 2131, 2311, 10531
Offset: 1

Views

Author

Musab Akbas, Aug 22 2021

Keywords

Comments

a(6) > 10^10.
a(6) <= 2111111111111111111111113 (25 digits). - Jon E. Schoenfield, Aug 22 2021

Examples

			With 2113, omitting all instances of 1's gives 23, 2's gives 113, 3's gives 211, 1's and 2's gives 3, 1's and 3's gives 2, and 2's and 3's gives 11. All of these are prime numbers.

Crossrefs

Cf. A057876.
Showing 1-9 of 9 results.

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

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