A020465 Primes that contain digits 4 and 7 only.

7, 47, 4447, 7477, 44777, 47777, 74747, 77447, 77477, 77747, 4444747, 4447747, 4747747, 4774477, 4774747, 7444477, 7447777, 7474477, 7477777, 7747477, 7774777, 7777447, 44447747, 44747447, 44747777, 44774777, 47447747, 47774477, 47774747

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1000 terms from Vincenzo Librandi)
• James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)

Crossrefs

Cf. A284971.

Programs

Magma

[p: p in PrimesUpTo(47774747) | Set(Intseq(p)) subset [4, 7]]; // Vincenzo Librandi, Jul 27 2012

Mathematica

Flatten[Table[Select[FromDigits/@Tuples[{4,7},n],PrimeQ],{n,8}]] (* Vincenzo Librandi, Jul 27 2012 *)

Python

from sympy import isprime
from itertools import count, takewhile
def A284971(n):
  b = bin(n+1)[3:]
  return int("".join(b.replace("0", "4").replace("1", "7")))
def aupto(limit):
  return list(filter(isprime, takewhile(lambda x: x <= limit, (A284971(n) for n in count(1)))))
print(aupto(47774747)) # Michael S. Branicky, Apr 07 2021