A077719 Primes which can be expressed as sum of distinct powers of 5.

5, 31, 131, 151, 631, 751, 3251, 3881, 16381, 19381, 19501, 19531, 78781, 78901, 81281, 81401, 81901, 82031, 93901, 94531, 97001, 97501, 97651, 390751, 390781, 393901, 394501, 406381, 468781, 469501, 471901, 472631, 484531, 485131, 487651, 1953151, 1953901

Offset: 1

Author

Amarnath Murthy, Nov 19 2002

Keywords

• nonn

Comments

Primes whose base 5 representation contains only zeros and 1's.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020449, A000695, A033042, A077717, A077718, A077720, A077721, A077722.

Programs

Python

from sympy import isprime
def aupton(terms):
  k, alst = 0, []
  while len(alst) < terms:
    k += 1
    t = sum(5**i*int(di) for i, di in enumerate((bin(k)[2:])[::-1]))
    if isprime(t): alst.append(t)
  return alst
print(aupton(37)) # Michael S. Branicky, May 31 2021

Extensions

More terms from Sascha Kurz, Jan 03 2003

a(36) and beyond from Michael S. Branicky, May 31 2021