A199340 - OEIS

%I #21 Sep 08 2022 08:46:00

%S 3,43,433,443,3343,3433,4003,30403,33343,33403,34033,34303,34403,

%T 40343,40433,43003,43403,300043,300343,304033,304303,304433,330433,

%U 333433,334043,334333,334403,343303,343333,343433,400033,403003,403043,403433,430303,430333

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

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

%C A020461 is a subsequence. - _Vincenzo Librandi_, Jul 23 2015

%H Alois P. Heinz, <a href="/A199340/b199340.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#PrimesWithDigits">Index to entries about primes with digits in a given set</a>.

%t Select[Prime[Range[5 10^4]], Complement[IntegerDigits[#], {3, 4, 0}]=={} &] (* _Vincenzo Librandi_, Jul 23 2015 *)

%t Select[FromDigits/@Tuples[{0,3,4},6],PrimeQ] (* _Harvey P. Dale_, Mar 21 2020 *)

%t Select[10#+3&/@FromDigits/@Tuples[{0,3,4},5],PrimeQ] (* _Harvey P. Dale_, May 02 2022 *)

%o (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

%o (Magma) [p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [3, 4, 0]]; // _Vincenzo Librandi_, Jul 23 2015

%o (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

%Y 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).

%Y Cf. A020449 - A020472, A199325 - A199329.

%Y Cf. A058429, A058430.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Nov 05 2011