A129910 Quotient of the decimal representation of concatenated twin primes in reverse divided by 3.

17, 25, 437, 639, 1043, 1447, 2053, 2457, 34367, 36369, 46379, 50383, 60393, 64397, 66399, 76409, 80413, 90423, 94427, 104437, 116449, 140473, 144477, 154487, 174507, 190523, 200533, 206539, 214547, 220553, 270603, 274607, 276609, 286619

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

Sequence in context: A183346 A166666 A147445 * A259075 A212909 A273785

Adjacent sequences: A129907 A129908 A129909 * A129911 A129912 A129913

Keyword

base,frac,nonn

Author

Cino Hilliard, Jun 05 2007

Status

approved