A261135 - OEIS

%I #12 Aug 20 2015 16:00:25

%S 1,22,475,20188,1472229,112441134,8415721847,1234163177336,

%T 336405959636873,95454487901599898,26891544907776231851,

%U 7513814442828887530172,2084725487959034609380301,574954374994698424018451678,157752074714160807772190133743,86177704805459827544499089423856

%N 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 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 a(1) = binary_to_decimal(1) = 1;

%e a(2) = binary_to_decimal(10110) = 22;

%e a(3) = binary_to_decimal(111011011) = 475;

%e a(4) = binary_to_decimal(100111011011100) = 20188.

%t Table[d = IntegerDigits[#, 2] & /@ Range@ n; FromDigits[#, 2] &@

%t Flatten[{Flatten@ Reverse@ d, Flatten@ Rest@ d}, 1], {n, 16}] (* _Michael De Vlieger_, Aug 20 2015 *)

%Y Cf. A007942 for a base-10 version.

%Y Cf. A173427 for an inverted ordering of repeated binary numbers.

%K nonn,base

%O 1,2

%A _Umut Uludag_, Aug 10 2015

%E a(11)-a(16) from _Michael De Vlieger_, Aug 20 2015