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%I #10 Feb 18 2023 14:25:26
%S 2,4,24,16,80,192,896,256,1152,2560,11264,12288,53248,114688,491520,
%T 65536,278528,589824,2490368,2621440,11010048,23068672,96468992,
%U 50331648,209715200,436207616,1811939328,1879048192,7784628224,16106127360,66571993088,4294967296
%N a(n) is the smallest positive integer m with exactly n zeros in its binary representation and with n represented in binary as a substring of the binary representation of m.
%C a(3315) has 1001 digits. - _Michael S. Branicky_, Feb 18 2023
%H Michael S. Branicky, <a href="/A147761/b147761.txt">Table of n, a(n) for n = 1..3314</a>
%F a(n) = n*2^(n-A023416(n)). - _Michael S. Branicky_, Feb 18 2023
%e 5 represented in binary is 101. 80 represented in binary is 1010000, which contains exactly five 0's and 101 as a substring ({101}0000). Since 80 is the smallest positive integer that satisfies the conditions, then a(5) = 80.
%o (Python)
%o def a(n): b = bin(n)[2:]; return n << (n - b.count("0"))
%o print([a(n) for n in range(1, 33)]) # _Michael S. Branicky_, Feb 18 2023
%Y Cf. A023416, A147760, A147762.
%K base,nonn
%O 1,1
%A _Leroy Quet_, Nov 11 2008
%E Extended by _Ray Chandler_, Nov 15 2008
%E a(30) and beyond from _Michael S. Branicky_, Feb 18 2023