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

1,1

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A073064.

Sequence in context: A158051 A091366 A073064 * A180421 A176179 A176196

Adjacent sequences: A155072 A155073 A155074 * A155076 A155077 A155078

Keyword

nonn,fini,base

Author

Juri-Stepan Gerasimov, Jan 19 2009

Extensions

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

Status

approved