login
Decimal values a(n) of the binary numbers b(n) obtained by starting from first prime number (2), sequentially concatenating the binary representation of all prime numbers till n-th prime, and after that, sequentially concatenating the binary representation of all prime numbers, from (n-1)th till the first prime.
0

%I #3 Jul 12 2012 00:39:51

%S 2,46,1502,96222,12316638,3153031134,1614350348254,1653094690025438,

%T 1692768964130074590,1733395419356639752158,1774996909423485572837342,

%U 3635193670499109531489365982

%N Decimal values a(n) of the binary numbers b(n) obtained by starting from first prime number (2), sequentially concatenating the binary representation of all prime numbers till n-th prime, and after that, sequentially concatenating the binary representation of all prime numbers, from (n-1)th till the first prime.

%F a(n) = binary_to_decimal(concatenate(10, 11, 101, ..., binary((n-2)th prime), binary((n-1)th prime), binary(n-th prime), binary((n-1)th prime), binary((n-2)th prime), ..., 101, 11, 10))

%e a(1)=binary_to_decimal(10)=2, a(2)=binary_to_decimal(101110)=46, a(3)=binary_to_decimal(10111011110)=1502, a(4)=binary_to_decimal(10111011111011110)=96222 etc.

%Y Cf. A066622. This sequence uses the term generation rule of A066622 (Concatenation of prime numbers in increasing order up to the n-th and then in decreasing order.), albeit with the binary base instead of the decimal base.

%K base,nonn

%O 1,1

%A _Umut Uludag_, Feb 22 2010