A035059 Numbers k such that 2^k does not contain the digit 4 (probably finite).

0, 1, 3, 4, 5, 7, 8, 9, 13, 15, 16, 17, 21, 23, 24, 29, 40, 41, 43, 55, 69, 75, 85, 107

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base
• more

Comments

a(25) > 2*10^9 if it exists. - Jon E. Schoenfield and Michael S. Branicky, Aug 02 2021

Crossrefs

Cf. similar sequences listed in A035064.

Programs

Magma

[n: n in [0..1000] | not 4 in Intseq(2^n) ]; // Vincenzo Librandi, May 07 2015

Mathematica

Join[{0}, Select[Range@10000, FreeQ[IntegerDigits[2^#], 4] &]] (* Vincenzo Librandi, May 07 2015 *)

Python

N = 200; modder = 10**N; REPORT = 10**5
def ok(s):  return '4' not in s
def ok1(n): return ok(str(pow(2, n, modder)))
def afind(limit, startk=0, verbose=False):
    full_tests = 0
    for k in range(startk, limit):
        if ok1(k):
            full_tests += 1
            if ok(str(pow(2, k))): print(k, end=", ")
        if verbose and k and k%REPORT == 0:
            print("[ ...", k, full_tests, "]")
        k += 1
afind(10**6, verbose=True) # Michael S. Branicky, Aug 02 2021

Extensions

Initial 0 inserted by Vincenzo Librandi, May 07 2015