A155075 Primes with one digit used exactly twice, all others digits distinct.

11, 101, 113, 131, 151, 181, 191, 199, 211, 223, 227, 229, 233, 277, 311, 313, 331, 337, 353, 373, 383, 433, 443, 449, 499, 557, 577, 599, 661, 677, 727, 733, 757, 773, 787, 797, 811, 877, 881, 883, 887, 911, 919, 929, 977, 991, 997, 1009, 1013, 1019, 1021

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 19 2009

Keywords

• nonn
• fini
• base

Comments

The sequence is finite. The last 10 terms are 98876342501, 98876405231, 98876421053, 98876502143, 98876504123, 98876520143, 98876524013, 98876524301, 98876530421, 98876532401. - Zak Seidov, Dec 18 2014

Number of n-digits terms starting with n=1: {0, 1, 46, 508, 4117, 31395, 187533, 854665, 2989094, 7172381, 6481542}. - Zak Seidov, Jun 04 2015

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A073064.

Programs

Maple

G:= proc(d) # to produce all d-digit terms
  local L, C, Cc, P, i, x, res;
  res:= NULL;
  L:= [false, true, false, true, false, false, false, true, false, true];
  for C in  combinat:-choose([$0..9], d-1) do
    for i from 1 to d-1 do
      Cc:= [op(C), C[i]];
      if convert(Cc, `+`) mod 3 = 0 then next fi;
      for P in combinat:-permute(Cc) do
        if P[-1] = 0 or not L[P[1]+1] then next fi;
        x:= add(P[i]*10^(i-1), i=1..nops(P));
        if isprime(x) then res:= res, x fi;
      od
    od
  od;
  sort([res]);
end proc:
seq(op(G(d)), d=1..5); # Robert Israel, Jun 04 2015

Mathematica

fQ[n_]:=Length[IntegerDigits[n]]-Length[Union[IntegerDigits[n]]]==1;Select[Prime@Range[21713],fQ[#]&] (* Ivan N. Ianakiev, Sep 25 2015 *)

PARI

lista(nn) = {forprime(p=2, nn, my(d = digits(p)); if (#vecsort(d,,8) == #d-1, print1(p, ", ")););} \\ Michel Marcus, Dec 18 2014

Extensions

Definition clarified by R. J. Mathar, May 05 2010