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A372680 Integers k such that 2^k contains all powers of 2 not exceeding k as substrings.

%I A372680 #13 May 10 2024 11:12:00
%S A372680 124,192,322,808,830,957,1757,4067,5489,6616,6724,6794,7065,7727,7728,
%T A372680 7736,8253,8938,9438,9989,10194,10195,10271,10350,10389,10397,10445,
%U A372680 10475,10611,10835,11107,11500,11606,11758,11835,12089,12304,12398,12501,12548,12645,12694,12695,12734,12820
%N A372680 Integers k such that 2^k contains all powers of 2 not exceeding k as substrings.
%C A372680 It is unknown whether this sequence contains infinitely many terms.
%e A372680 124 is a term; 2^124 = 21267647932558653966460912964485513216 contains 2, 4, 8, 16, 32, 64 as substrings.
%o A372680 (Python)
%o A372680 def f(m):
%o A372680   a = str(2**m)
%o A372680   for i in range(0, m.bit_length()):
%o A372680     if str(2**i) not in a:
%o A372680       return 0
%o A372680   return 1
%o A372680 def a(n):
%o A372680   m = 0
%o A372680   i = 0
%o A372680   while i != n:
%o A372680     m += 1
%o A372680     i += f(m)
%o A372680   return m
%Y A372680 Cf. A046300, A094776, A371808.
%K A372680 nonn,base
%O A372680 1,1
%A A372680 _Bryle Morga_, May 10 2024