A199341 Primes having only the (decimal) digits 1, 3 and 4.

3, 11, 13, 31, 41, 43, 113, 131, 311, 313, 331, 431, 433, 443, 1433, 3313, 3331, 3343, 3413, 3433, 4111, 4133, 4441, 11113, 11131, 11311, 11411, 11443, 13313, 13331, 13411, 13441, 14143, 14341, 14411, 14431, 31333, 33113, 33311, 33331, 33343, 33413, 34141, 34313

Offset

1,1

Comments

A020451, A020452 and A020461 are subsequences. - Vincenzo Librandi, Jul 26 2015

Links

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

Andrew Granville, Missing digits, and good approximations, arXiv:2308.03126 [math.NT], 2023. See p. 4.

Maple

Dmax:= 5: # to get all terms < 10^Dmax
Cd:= {1, 3, 4}:
C:= Cd:
for d from 2 to Dmax do
  Cd:= map(t -> (10*t+1, 10*t+3, 10*t+4), Cd);
  C:= C union Cd;
od:
sort(convert(select(isprime, C), list)); # Robert Israel, Jul 26 2015

Mathematica

Select[Prime[Range[4 10^3]], Complement[IntegerDigits[#], {3, 4, 1}]=={} &] (* Vincenzo Librandi, Jul 26 2015 *)

Prog

(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)))}
(Magma) [p: p in PrimesUpTo(10^5) | Set(Intseq(p)) subset [3, 4, 1]]; // Vincenzo Librandi, Jul 26 2015

Crossrefs

Cf. A020449 - A020472, A199325 - A199329.

Cf. similar sequences listed in A199340.

Sequence in context: A032917 A006559 A023248 * A111488 A125308 A260044

Adjacent sequences: A199338 A199339 A199340 * A199342 A199343 A199344

Keyword

nonn,base

Author

M. F. Hasler, Nov 05 2011

Status

approved