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A129908 Quotient of the decimal representation of concatenated twin primes divided by 3. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A129909 A174976 A003284

Adjacent sequences:  A129905 A129906 A129907 * A129909 A129910 A129911

KEYWORD

base,frac,nonn

AUTHOR

Cino Hilliard, Jun 05 2007

STATUS

approved

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Last modified May 22 21:00 EDT 2019. Contains 323491 sequences. (Running on oeis4.)