Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Jul 21 2022 03:07:24
%S 3,7,9,10,12,15,19,21,25,31,34,36,37,40,41,42,45,46,54,56,58,63,69,73,
%T 77,81,85,89,91,99,109,127,132,136,137,141,142,144,145,146,148,150,
%U 151,153,154,157,165,166,167,170,173,175,177,178,181,182,184,185,187
%N Numbers such that every bit in its binary expansion is in a substring of length A342263(n) that appears more than once.
%C This list contains all terms of the form 2^n - 1 for n >= 2.
%e The binary expansion of 8501 is 10000100110101, and there are A354614(8501) = 5 repeated substrings of length A342263(8501) = 3: 101, 100, 010, 001, and 000. Every bit in the binary expansion of 8501 appears in one or more of these substrings, so 8501 is in the list.
%e 10000100110101
%e .........101..
%e ...........101
%e 100...........
%e .....100......
%e ....010.......
%e ..........010.
%e ...001........
%e ......001.....
%e .000..........
%e ..000.........
%Y Cf. A342263, A354614.
%K base,nonn
%O 1,1
%A _Peter Kagey_, Jul 08 2022