A020455 Primes that contain digits 1 and 7 only.

7, 11, 17, 71, 1117, 1171, 1777, 7177, 7717, 11117, 11171, 11177, 11717, 11777, 17117, 71171, 71711, 71777, 77171, 77711, 1111711, 1111771, 1117111, 1117117, 1117177, 1171111, 1171117, 1171771, 1177171, 1177711, 1177717, 1711117, 1717117, 1771177, 1771717

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Comments

There are no terms whose number of digits is divisible by 3: for every d that is a multiple of 3, every d-digit number j consisting of no digits other than 1's and 7's will have a digit sum divisible by 3, so j will also be divisible by 3. - Mikk Heidemaa, Mar 26 2021

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

Subsequence of A030096.

Cf. A000040, A276039.

Programs

Magma

[p: p in PrimesUpTo(1771177) | Set(Intseq(p)) subset [1, 7]]; // Vincenzo Librandi, Jul 27 2012

Mathematica

Flatten[Table[Select[FromDigits/@Tuples[{1,7},n],PrimeQ],{n,7}]] (* Vincenzo Librandi, Jul 27 2012 *)

Python

from sympy import isprime
def only17(n): return int(bin(n+1)[3:].replace('1', '7').replace('0', '1'))
def auptod(digs):
  return list(filter(isprime, (only17(i) for i in range(1, 2**(digs+1)-1))))
print(auptod(8)) # Michael S. Branicky, Jul 11 2021

Formula

{ A000040 } intersect { A276039 }.