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.

1, 22, 475, 20188, 1472229, 112441134, 8415721847, 1234163177336, 336405959636873, 95454487901599898, 26891544907776231851, 7513814442828887530172, 2084725487959034609380301, 574954374994698424018451678, 157752074714160807772190133743, 86177704805459827544499089423856

Offset: 1

Author

Umut Uludag, Aug 10 2015

Keywords

• nonn
• base

Examples

			a(1) = binary_to_decimal(1) = 1;
a(2) = binary_to_decimal(10110) = 22;
a(3) = binary_to_decimal(111011011) = 475;
a(4) = binary_to_decimal(100111011011100) = 20188.
		

Crossrefs

Cf. A007942 for a base-10 version.

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

Programs

Mathematica

Table[d = IntegerDigits[#, 2] & /@ Range@ n; FromDigits[#, 2] &@
Flatten[{Flatten@ Reverse@ d, Flatten@ Rest@ d}, 1], {n, 16}] (* Michael De Vlieger, Aug 20 2015 *)

Formula

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)))

Extensions

a(11)-a(16) from Michael De Vlieger, Aug 20 2015