A073064 -id:A073064 - cp's OEIS frontend

A073069 Indices of primes with non-distinct digits.

5, 26, 30, 32, 36, 42, 43, 46, 47, 48, 49, 50, 51, 59, 64, 65, 67, 68, 71, 74, 76, 84, 86, 87, 95, 102, 106, 109, 121, 123, 129, 130, 134, 137, 138, 139, 141, 151, 152, 153, 154, 156, 157, 158, 165, 167, 168, 169, 170, 171, 172, 173, 174, 177, 178, 182, 185, 186

Offset: 1

Zak Seidov Aug 24 2002

Indices of primes in A073064. Cf. A030291.

ta=IntegerDigits[Prime[Range[1000]]]; ta2=Table[Length[ta[[i]]]>Length[Union[ta[[i]]]], {i, 1000}]; Flatten[Position[ta2, True]]

from sympy import prime, primerange
def ok(p): s = str(p); return len(set(s)) < len(s)
def aupto(limit):
  alst = []
  for pi, p in enumerate(primerange(1, prime(limit)+1), start = 1):
    if ok(p): alst.append(pi)
  return alst
print(aupto(186)) # Michael S. Branicky, May 26 2021

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

Original entry on oeis.org

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

Juri-Stepan Gerasimov, Jan 19 2009

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

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

Cf. A000040, A073064.

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

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

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

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

cp's OEIS Frontend

A073069 Indices of primes with non-distinct digits.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions