

A129910


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 6k1. So concatenation in decimal is (6k+1) *10^d + 6k1 = 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.


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



