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Search: id:A087732
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| A087732 |
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Smaller of twin primes of the form P=j*P(i)#-1 and P=j*P(i)#+1 with 0 < j < P(i+1), where P(i) denotes i-th prime and P(i)# the i-th primorial number A002110(i). |
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+0
6
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| 3, 5, 11, 17, 29, 59, 149, 179, 419, 1049, 2309, 9239, 11549, 25409, 180179, 270269, 300299, 330329, 390389, 420419, 4084079, 8678669, 106696589, 892371479, 2454021569, 3569485919, 4238764529, 4461857399, 4908043139, 6023507489
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Probably an infinite sequence. Using the UB874 program (UBASIC) I found the first 123 primes of the sequence for i <= 382. I think I have a proof that the sequence is infinite.
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EXAMPLE
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17=3*P(2)#-1 and 19=3*P(2)#+1 are twin primes, so 17 is in the sequence, corresponding to i=2, j=3. Again, 182*2633#-1 and 182*2633#+1 are prime twins, with j=182, i=382. These are 1111-digit twin primes.
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CROSSREFS
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Cf. A000040, A002110, A086916, A087700, A087731, A088676.
Sequence in context: A129694 A108402 A090795 this_sequence A108542 A006450 A085918
Adjacent sequences: A087729 A087730 A087731 this_sequence A087733 A087734 A087735
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KEYWORD
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nonn
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AUTHOR
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Pierre CAMI (colettecami(AT)aol.com), Sep 29 2003
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EXTENSIONS
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Edited by Jud McCranie (judmccr(AT)bellsouth.net), Oct 06, 2003
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 15 2006
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