A122467 - OEIS

%I #6 Mar 30 2012 18:40:38

%S 100,210,1211,2221,3331,4442,14543,24653,35654,46664,146665,246675,

%T 346686,446796,546907,648017,758018,868029,978140,1089141,1200151,

%U 1311261,2311262,3311363,4312373,5313474,6323484,7333585,8343695

%N Write n-th semiprime in binary, sum as if decimal numbers.

%C Partial sum of A122466. Write n-th semiprime in binary, sum as if decimal numbers. Primes in this sequence begin a(4) = 2221, a(5) = 3331, a(7) = 14543 and a(34) = 13398139.

%F a(n) = SUM[i=1..n]A122466(i) = SUM[i=1..n]A007088(A001358(i)).

%e a(4) = 100 + 110 + 1001 + 1010 = 2221 because the first 4 semiprimes can be written in binary as 100_2 + 110_2 + 1001_2 + 1010_2.

%e a(34) = 100 + 110 + 1001 + 1010 + 1110 + 1111 + 10101 + 10110 + 11001 + 11010 + 100001 + 100010 + 100011 + 100110 + 100111 + 101110 + 110001 + 110011 + 110111 + 111001 + 111010 + 111110 + 1000001 + 1000101 + 1001010 + 1001101 + 1010010 + 1010101 + 1010110 + 1010111 + 1011011 + 1011101 + 1011110 + 1011111 = 13398139 is prime.

%Y Cf. A000040, A001358, A007088, A004676, A122466.

%K base,easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Sep 09 2006