A199340 Primes having only the (decimal) digits 0, 3 and 4.

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

1,1

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.

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 *)

Prog

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

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.

Sequence in context: A199349 A197609 A199346 * A020461 A138974 A036940

Adjacent sequences: A199337 A199338 A199339 * A199341 A199342 A199343

Keyword

nonn,base

Author

M. F. Hasler, Nov 05 2011

Status

approved