A129908 Quotient of the decimal representation of concatenated twin primes divided by 3.

11, 19, 371, 573, 977, 1381, 1987, 2391, 33701, 35703, 45713, 49717, 59727, 63731, 65733, 75743, 79747, 89757, 93761, 103771, 115783, 139807, 143811, 153821, 173841, 189857, 199867, 205873, 213881, 219887, 269937, 273941, 275943, 285953

Offset

1,1

Comments

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 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 quotient of 35/3 is 11 which is the first term.

Mathematica

Join[{11}, FromDigits[Flatten[IntegerDigits/@#]]/3&/@Rest[Select[ Partition[ Prime[ Range[200]], 2, 1], Last[#]-First[#]==2&]]] (* Harvey P. Dale, Oct 12 2012 *)

Prog

(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", ")) ) }

Crossrefs

Sequence in context: A020457 A032370 A295834 * A344431 A129909 A174976

Adjacent sequences: A129905 A129906 A129907 * A129909 A129910 A129911

Keyword

base,frac,nonn

Author

Cino Hilliard, Jun 05 2007

Status

approved