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A135508
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a(n)=x(n+1)/x(n)-2 where x(1)=1 and x(n)=2*x(n-1)+lcm(x(n-1),n).
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12
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2, 3, 1, 1, 1, 7, 2, 1, 1, 11, 1, 1, 7, 1, 1, 17, 1, 1, 1, 7, 11, 23, 1, 1, 1, 1, 7, 29, 1, 1, 2, 11, 17, 7, 1, 37, 1, 1, 1, 41, 7, 1, 11, 1, 23, 47, 1, 1, 1, 17, 1, 53, 1, 1, 1, 1, 29, 59, 1, 1, 1, 1, 1, 1, 1, 67, 17, 1, 1, 71, 1, 1, 37, 1, 1, 1, 1, 79, 1, 1, 41, 83, 1, 1, 1, 29, 1, 89, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This sequence has fascinating properties related to primes and especially to twin primes. For instance sequence consists of 1's or primes only. 2 occurs infinitely many times, largest primes in twin pairs never occur, other primes occur finitely many times...
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REFERENCES
| Benoit Cloitre, Beyond Rowland's gcd sequence, in preparation, 2008
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LINKS
| Markus Schepke, Uber Primzahlerzeugende Folgen, Thesis, U. Hannover, 2009
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FORMULA
| a(2*4^k)=2 k>=0
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PROG
| (PARI) x1=1; for(n=2, 40, x2=2*x1+lcm(x1, n); t=x1; x1=x2; print1(x2/t-2, ", "))
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CROSSREFS
| Cf. A106108.
Sequence in context: A106178 A205104 A108714 * A030413 A139434 A113925
Adjacent sequences: A135505 A135506 A135507 * A135509 A135510 A135511
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 09 2008
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