A172404 Numbers k such that 3 is the first digit of 2^k.

5, 15, 25, 35, 45, 55, 65, 75, 78, 85, 88, 95, 98, 108, 118, 128, 138, 148, 158, 168, 178, 181, 188, 191, 201, 211, 221, 231, 241, 251, 261, 271, 274, 281, 284, 291, 294, 304, 314, 324, 334, 344, 354, 364, 367, 374, 377, 384, 387, 397, 407, 417, 427, 437, 447, 457, 467, 470, 477, 480, 487, 490, 500

Offset: 1

Author

David Radcliffe, Nov 20 2010

Keywords

• nonn
• base
• easy

Comments

The asymptotic density of this sequence is log_10(4/3) = 0.124938... - Amiram Eldar, Jan 27 2021

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (first 4200 terms from Muniru A Asiru)

Crossrefs

Cf. A000079.

Cf. A067497, A067469, A367294, A363060, A367295, A330243, A367296, A097415.

Programs

GAP

Filtered([1..500],n->ListOfDigits(2^n)[1]=3); # Muniru A Asiru, Oct 17 2018

Maple

x := 1.; L := []; for n from 0 to 500 do if 3 < x and x < 4 then L := [op(L), n] end if; x := 2*x; if x > 10 then x := (1/10)*x end if end do; L;

Mathematica

Select[Range[1000], IntegerDigits[2^#][[1]] == 3 &]

PARI

isok(n) = digits(2^n)[1] == 3; \\ Michel Marcus, Oct 18 2018

Python

ans, x = [], 1.
for n in range(501):
    if 3 < x < 4: ans.append(n)
    x = x*2
    if x > 10: x = x / 10
print(ans)

Python

from itertools import islice
def A172404_gen(): # generator of terms
    a, b, c, l = 3, 4, 1, 0
    while True:
        if a<=c:
            if cA172404_list = list(islice(A172404_gen(),30)) # Chai Wah Wu, Nov 13 2023