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%I #4 Mar 02 2018 17:35:50
%S 17,25,437,639,1043,1447,2053,2457,34367,36369,46379,50383,60393,
%T 64397,66399,76409,80413,90423,94427,104437,116449,140473,144477,
%U 154487,174507,190523,200533,206539,214547,220553,270603,274607,276609,286619
%N Quotient of the decimal representation of concatenated twin primes in reverse divided by 3.
%C Except for the first term, concatenated twin primes reversed are always divisible by 3. This follows from the fact that twin prime components > 3 in reverse are of the form 6k+1 and 6k-1. So concatenation in decimal is (6k+1) *10^d + 6k-1 = 6k(10^d+1)+(10^d-1) where d is the number of digits in each twin prime component. Now 10^d-1 = (10-1)(10^(d-1)+10^(d-2)+...+1) = 9h and 6k(10^d+1) + 9h is divided by 3.
%H Harvey P. Dale, <a href="/A129910/b129910.txt">Table of n, a(n) for n = 1..1000</a>
%e The first concatenated twin prime pair in decimal representation is 35. The reverse is 53. The quotient of 53/3 is 17 which is the first term.
%t qdr[{a_,b_}]:=Quotient[FromDigits[Flatten[IntegerDigits/@{b,a}]],3]; qdr/@ Select[Partition[Prime[Range[200]],2,1],#[[2]]-#[[1]]==2&] (* _Harvey P. Dale_, Mar 02 2018 *)
%o (PARI) concattwins3r(n) = { local(x,y); forprime(x=2,n, if(isprime(x+2), y=floor(eval(concat(Str(x+2),Str(x)))/3); print1(y",") ) ) }
%K base,frac,nonn
%O 1,1
%A _Cino Hilliard_, Jun 05 2007