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Integers k such that 2^k contains all powers of 2 not exceeding k as substrings.
0

%I #13 May 10 2024 11:12:00

%S 124,192,322,808,830,957,1757,4067,5489,6616,6724,6794,7065,7727,7728,

%T 7736,8253,8938,9438,9989,10194,10195,10271,10350,10389,10397,10445,

%U 10475,10611,10835,11107,11500,11606,11758,11835,12089,12304,12398,12501,12548,12645,12694,12695,12734,12820

%N Integers k such that 2^k contains all powers of 2 not exceeding k as substrings.

%C It is unknown whether this sequence contains infinitely many terms.

%e 124 is a term; 2^124 = 21267647932558653966460912964485513216 contains 2, 4, 8, 16, 32, 64 as substrings.

%o (Python)

%o def f(m):

%o a = str(2**m)

%o for i in range(0, m.bit_length()):

%o if str(2**i) not in a:

%o return 0

%o return 1

%o def a(n):

%o m = 0

%o i = 0

%o while i != n:

%o m += 1

%o i += f(m)

%o return m

%Y Cf. A046300, A094776, A371808.

%K nonn,base

%O 1,1

%A _Bryle Morga_, May 10 2024