%I
%S 11,19,371,573,977,1381,1987,2391,33701,35703,45713,49717,59727,63731,
%T 65733,75743,79747,89757,93761,103771,115783,139807,143811,153821,
%U 173841,189857,199867,205873,213881,219887,269937,273941,275943,285953
%N Quotient of the decimal representation of concatenated twin primes divided by 3.
%C Except for the first term, concatenated twin primes are always divisible by 3. This follows from the fact that twin prime components > 3 are of the form 6k1 and 6k+1. So concatenation in decimal is (6k1)*10^d + 6k+1 = 6k(10^d+1)+(10^d1) where d is the number of digits in each twin prime component. Now 10^d1 = (101)(10^(d1)+10^(d2)+...+1) = 9h and 6k(10^d+1) + 9h is divided by 3.
%H Harvey P. Dale, <a href="/A129908/b129908.txt">Table of n, a(n) for n = 1..1000</a>
%e The first concatenated twin prime pair in decimal representation is 35.
%e The quotient of 35/3 is 11 which is the first term.
%t Join[{11},FromDigits[Flatten[IntegerDigits/@#]]/3&/@Rest[Select[ Partition[ Prime[ Range[200]],2,1],Last[#]First[#]==2&]]] (* _Harvey P. Dale_, Oct 12 2012 *)
%o (PARI) concattwins3(n) = { local(x,y); forprime(x=2,n, if(isprime(x+2), y=eval(concat(Str(x),Str(x+2)))/3; print1(y",")) ) }
%K base,frac,nonn
%O 1,1
%A _Cino Hilliard_, Jun 05 2007
