|
%I #15 Aug 08 2023 04:47:31
%S 3,11,13,31,41,43,113,131,311,313,331,431,433,443,1433,3313,3331,3343,
%T 3413,3433,4111,4133,4441,11113,11131,11311,11411,11443,13313,13331,
%U 13411,13441,14143,14341,14411,14431,31333,33113,33311,33331,33343,33413,34141,34313
%N Primes having only the (decimal) digits 1, 3 and 4.
%C A020451, A020452 and A020461 are subsequences. - _Vincenzo Librandi_, Jul 26 2015
%H Robert Israel, <a href="/A199341/b199341.txt">Table of n, a(n) for n = 1..10000</a>
%H Andrew Granville, <a href="https://arxiv.org/abs/2308.03126">Missing digits, and good approximations</a>, arXiv:2308.03126 [math.NT], 2023. See p. 4.
%p Dmax:= 5: # to get all terms < 10^Dmax
%p Cd:= {1,3,4}:
%p C:= Cd:
%p for d from 2 to Dmax do
%p Cd:= map(t -> (10*t+1,10*t+3,10*t+4),Cd);
%p C:= C union Cd;
%p od:
%p sort(convert(select(isprime,C),list)); # _Robert Israel_, Jul 26 2015
%t Select[Prime[Range[4 10^3]], Complement[IntegerDigits[#], {3, 4, 1}]=={} &] (* _Vincenzo Librandi_, Jul 26 2015 *)
%o (PARI) a(n, list=0, L=[1, 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)))}
%o (Magma) [p: p in PrimesUpTo(10^5) | Set(Intseq(p)) subset [3, 4, 1]]; // _Vincenzo Librandi_, Jul 26 2015
%Y Cf. A020449 - A020472, A199325 - A199329.
%Y Cf. similar sequences listed in A199340.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Nov 05 2011
|
