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Search: id:A129910
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| A129910 |
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Quotient of the decimal representation of concatenated twin primes in reverse divided by 3. |
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+0
2
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| 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; 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 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 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 reverse is 53. The quotient of 53/3 is 17 which is the first term.
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PROGRAM
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(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", ") ) ) }
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CROSSREFS
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Sequence in context: A082130 A140609 A131275 this_sequence A034963 A120143 A031204
Adjacent sequences: A129907 A129908 A129909 this_sequence A129911 A129912 A129913
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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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