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a(n) = the smallest positive integer that contains more digits written in binary than n has written in binary, and which does not contain binary n as a substring in its binary representation.
0

%I #10 Jul 04 2021 07:50:16

%S 7,4,10,8,8,8,18,16,16,16,16,16,16,16,34,32,32,32,32,32,32,32,32,32,

%T 32,32,32,32,32,32,66,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,

%U 64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,130,128,128,128,128,128,128

%N a(n) = the smallest positive integer that contains more digits written in binary than n has written in binary, and which does not contain binary n as a substring in its binary representation.

%F a(2) = 7. For n >=2: a(2^n) = 2^(n+1) + 2; for m such that 2^(n-1)+1 <= m <= 2^n-1, a(m) = 2^n.

%o (Python)

%o def a(n):

%o if n == 2: return 7

%o digs = n.bit_length()

%o return int(2**digs) if n != 2**(digs - 1) else int(2**digs + 2)

%o print([a(n) for n in range(2, 71)]) # _Michael S. Branicky_, Jul 04 2021

%K base,easy,nonn

%O 2,1

%A _Leroy Quet_, Sep 17 2009

%E Extended by _Ray Chandler_, Mar 13 2010