This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A261135 #12 Aug 20 2015 16:00:25
%S A261135 1,22,475,20188,1472229,112441134,8415721847,1234163177336,
%T A261135 336405959636873,95454487901599898,26891544907776231851,
%U A261135 7513814442828887530172,2084725487959034609380301,574954374994698424018451678,157752074714160807772190133743,86177704805459827544499089423856
%N A261135 Decimal value a(n) of the binary number b(n) obtained by starting from n, sequentially concatenating all binary numbers down to 1 and then sequentially concatenating all binary numbers from 2 up to n.
%F A261135 a(n) = binary_to_decimal(concatenate(binary(n), binary(n-1), binary(n-2), ..., 11, 10, 1, 10, 11, ..., binary(n-2), binary(n-1), binary(n)))
%e A261135 a(1) = binary_to_decimal(1) = 1;
%e A261135 a(2) = binary_to_decimal(10110) = 22;
%e A261135 a(3) = binary_to_decimal(111011011) = 475;
%e A261135 a(4) = binary_to_decimal(100111011011100) = 20188.
%t A261135 Table[d = IntegerDigits[#, 2] & /@ Range@ n; FromDigits[#, 2] &@
%t A261135 Flatten[{Flatten@ Reverse@ d, Flatten@ Rest@ d}, 1], {n, 16}] (* _Michael De Vlieger_, Aug 20 2015 *)
%Y A261135 Cf. A007942 for a base-10 version.
%Y A261135 Cf. A173427 for an inverted ordering of repeated binary numbers.
%K A261135 nonn,base
%O A261135 1,2
%A A261135 _Umut Uludag_, Aug 10 2015
%E A261135 a(11)-a(16) from _Michael De Vlieger_, Aug 20 2015