A199327 Primes with digits '0', '1' and '7' only.

7, 11, 17, 71, 101, 107, 701, 1117, 1171, 1777, 7001, 7177, 7717, 10007, 10111, 10177, 10711, 10771, 11071, 11117, 11171, 11177, 11701, 11717, 11777, 17011, 17077, 17107, 17117, 17707, 70001, 70111, 70117, 70177, 70717, 71011, 71171, 71707, 71711, 71777, 77017, 77101, 77171, 77711, 101107, 101111, 101117

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).

Mathematica

f[i_, nn_]:=Select[Flatten[Table[FromDigits/@(Join[{i}, #]&/@Tuples[ {0, 1, 7}, n]), {n, 0, nn}]], PrimeQ]; Union[Join[f[1, 6], f[7, 6]]] (* Harvey P. Dale, Nov 19 2011 *)
Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {0, 1, 7}]=={}&] (* Vincenzo Librandi, Jan 16 2020 *)

Prog

(PARI) a(n, list=0, L=[0, 1, 7])={for(d=1, 1e9, my(t, u=vector(d, i, 10^(d-i))~); forvec(v=vector(d, i, [1+!(L[1]||(i>1&&i<d)), #L]), ispseudoprime( t=vecextract(L, v)*u)||next; list&&print1(t", "); n--||return(t)))} \\ Syntax updated for newer PARI versions by M. F. Hasler, Jul 26 2015
(Magma) [p: p in PrimesUpTo(80000) | Intseq(p) subset {0, 1, 7}]; // Vincenzo Librandi, Jan 16 2020

Crossrefs

Cf. A020449 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349.

Sequence in context: A167513 A260891 A276039 * A260892 A020455 A178617

Adjacent sequences: A199324 A199325 A199326 * A199328 A199329 A199330

Keyword

nonn,base

Author

M. F. Hasler, Nov 05 2011

Status

approved