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Primes that contain only the digits (3, 5, 8).
2

%I #9 Sep 08 2022 08:46:13

%S 3,5,53,83,353,383,853,883,3533,3583,3833,3853,5333,8353,33353,33533,

%T 35353,35533,38333,38833,53353,55333,83383,83833,85333,85853,88853,

%U 88883,333383,333533,335383,335833,338383,353333,353833,355853,383533,383833,533353

%N Primes that contain only the digits (3, 5, 8).

%C A020462 and A020464 are subsequences.

%H Alois P. Heinz, <a href="/A260226/b260226.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Prime[Range[5 10^4]], Complement[IntegerDigits[#], {3, 5, 8}]=={} &]

%t Select[Flatten[Table[FromDigits/@Tuples[{3,5,8},n],{n,6}]],PrimeQ] (* or *) Join[{3,5},Select[10#+3&/@Flatten[Table[FromDigits/@Tuples[{3,5,8},n],{n,5}]],PrimeQ]] (* The second program is faster because it recognizes that, except only for 5, each such prime must end in 3. *) (* _Harvey P. Dale_, Jul 17 2020 *)

%o (Magma) [p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [3, 5, 8]];

%Y Cf. similar sequences listed in A260223.

%Y Cf. A020462, A020464.

%K nonn,easy,base

%O 1,1

%A _Vincenzo Librandi_, Jul 22 2015