OFFSET
1,1
COMMENTS
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.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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", ") ) ) }
CROSSREFS
KEYWORD
base,frac,nonn
AUTHOR
Cino Hilliard, Jun 05 2007
STATUS
approved