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A020465 Primes that contain digits 4 and 7 only.

%I A020465 #21 Sep 08 2022 08:44:45
%S A020465 7,47,4447,7477,44777,47777,74747,77447,77477,77747,4444747,4447747,
%T A020465 4747747,4774477,4774747,7444477,7447777,7474477,7477777,7747477,
%U A020465 7774777,7777447,44447747,44747447,44747777,44774777,47447747,47774477,47774747
%N A020465 Primes that contain digits 4 and 7 only.
%H A020465 Alois P. Heinz, <a href="/A020465/b020465.txt">Table of n, a(n) for n = 1..20000</a> (first 1000 terms from Vincenzo Librandi)
%H A020465 James Maynard and Brady Haran, <a href="https://www.youtube.com/watch?v=eeoBCS7IEqs">Primes without a 7</a>, Numberphile video (2019)
%t A020465 Flatten[Table[Select[FromDigits/@Tuples[{4,7},n],PrimeQ],{n,8}]] (* _Vincenzo Librandi_, Jul 27 2012 *)
%o A020465 (Magma) [p: p in PrimesUpTo(47774747) | Set(Intseq(p)) subset [4, 7]]; // _Vincenzo Librandi_, Jul 27 2012
%o A020465 (Python)
%o A020465 from sympy import isprime
%o A020465 from itertools import count, takewhile
%o A020465 def A284971(n):
%o A020465   b = bin(n+1)[3:]
%o A020465   return int("".join(b.replace("0", "4").replace("1", "7")))
%o A020465 def aupto(limit):
%o A020465   return list(filter(isprime, takewhile(lambda x: x <= limit, (A284971(n) for n in count(1)))))
%o A020465 print(aupto(47774747)) # _Michael S. Branicky_, Apr 07 2021
%Y A020465 Cf. A284971.
%K A020465 nonn,base
%O A020465 1,1
%A A020465 _David W. Wilson_