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Search: id:A129909
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| A129909 |
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Primes that are the quotient of the decimal representation of concatenated twin primes divided by 3. |
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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EXAMPLE
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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.
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PROGRAM
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(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", ")) ) ) }
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CROSSREFS
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Adjacent sequences: A129906 A129907 A129908 this_sequence A129910 A129911 A129912
Sequence in context: A020457 A032370 A129908 this_sequence A003284 A063589 A102815
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KEYWORD
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base,frac,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Jun 05 2007
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