A165821 a(n) = the smallest positive integer that, when written in binary, contains both binary n and the binary representation of the n-th prime as substrings.

2, 6, 11, 28, 11, 13, 71, 152, 151, 58, 95, 101, 105, 174, 47, 848, 571, 978, 1075, 327, 1173, 719, 1335, 1432, 1561, 1626, 827, 860, 237, 241, 127, 131, 4233, 139, 4501, 1175, 4765, 2467, 167, 1384, 5299, 362, 703, 705, 1581, 1479, 3027, 3568, 227, 229