A199340 Primes having only {0, 3, 4} as digits.

3, 43, 433, 443, 3343, 3433, 4003, 30403, 33343, 33403, 34033, 34303, 34403, 40343, 40433, 43003, 43403, 300043, 300343, 304033, 304303, 304433, 330433, 333433, 334043, 334333, 334403, 343303, 343333, 343433, 400033, 403003, 403043, 403433, 430303, 430333

Offset: 1

Author

M. F. Hasler, Nov 05 2011

Keywords

• nonn
• base

Comments

All terms end in '3'. This could be used to speed up the given program.

A020461 is a subsequence. - Vincenzo Librandi, Jul 23 2015

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Index to entries about primes with digits in a given set.

Crossrefs

Cf. Primes that contain only the digits (3,4,k): this sequence (k=0), A199341 (k=1), A199342 (k=2), A199345 (k=5), A199346 (k=6), A199347 (k=7), A199348 (k=8), A199349 (k=9).

Cf. A020449 - A020472, A199325 - A199329.

Cf. A058429, A058430.

Programs

Magma

[p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [3, 4, 0]]; // Vincenzo Librandi, Jul 23 2015

Mathematica

Select[Prime[Range[5 10^4]], Complement[IntegerDigits[#], {3, 4, 0}]=={} &] (* Vincenzo Librandi, Jul 23 2015 *)
Select[FromDigits/@Tuples[{0,3,4},6],PrimeQ] (* Harvey P. Dale, Mar 21 2020 *)
Select[10#+3&/@FromDigits/@Tuples[{0,3,4},5],PrimeQ] (* Harvey P. Dale, May 02 2022 *)

PARI

a(n, list=0, L=[0, 3, 4], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal && !isprime(A004086(t)) && next; list && print1(t", "); n--||return(t)))} \\ Syntax updated for current PARI version. - M. F. Hasler, Jul 25 2015

PARI

{forprime(p=3,1e6,p%10==3&&!setminus(Set(digits(p)),[3,4])&&print1(p","))} \\ [0] evaluates to false. - M. F. Hasler, Jul 25 2015