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A129909 Primes that are the quotient of the decimal representation of concatenated twin primes divided by 3. 0
11, 19, 977, 1381, 1987, 75743, 93761, 115783, 213881, 273941, 285953, 4097077, 4337101, 4937161, 5737241, 6497317, 6757343, 8957563, 9097577, 10397707, 13057973, 14058073, 15158183, 15458213, 15998267, 17438411, 18338501 (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

Table of n, a(n) for n=1..27.

EXAMPLE

The first concatenated twin prime pair in decimal representation is 35.

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

PROG

(PARI) concattwins3p(n) = { local(x, y); forprime(x=2, n, if(isprime(x+2), y=eval(concat(Str(x), Str(x+2)))/3; if(isprime(y), print1(y", ")) ) ) }

CROSSREFS

Sequence in context: A032370 A295834 A129908 * A174976 A003284 A257401

Adjacent sequences:  A129906 A129907 A129908 * A129910 A129911 A129912

KEYWORD

base,frac,nonn

AUTHOR

Cino Hilliard, Jun 05 2007

STATUS

approved

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Last modified May 9 05:48 EDT 2021. Contains 343688 sequences. (Running on oeis4.)