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A166944
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a(1)=2, a(n)=a(n-1)+gcd(n, a(n-1)), if n is even, and a(n)=a(n-1)+ gcd(n-2, a(n-1)), if n is odd
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12
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2, 4, 5, 6, 9, 12, 13, 14, 21, 22, 23, 24, 25, 26, 39, 40, 45, 54, 55, 60, 61, 62, 63, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 129, 130, 135, 138, 139, 140, 147, 148, 149, 150, 151, 152, 153, 154, 155, 160, 161, 162, 163
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OFFSET
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1,1
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COMMENTS
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Conjecture. Every record of differences a(n)-a(n-1) more than 5 is greater of twin primes (A006512)
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REFERENCES
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E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol.11(2008), Article 08.2.8
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LINKS
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Table of n, a(n) for n=1..63.
V. Shevelev, A new generator of primes based on the Rowland idea [From Vladimir Shevelev, Oct 27 2009]
V. Shevelev, Three theorems on twin primes [From Vladimir Shevelev, Dec 03 2009]
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MAPLE
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A166944 := proc(n) option remember; if n = 1 then 2; else p := procname(n-1) ; if type(n, 'even') then p+igcd(n, p) ; else p+igcd(n-2, p) ; end if; end if; end proc: # R. J. Mathar, Sep 03 2011
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CROSSREFS
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Cf. A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293
Sequence in context: A047315 A125881 A089969 * A073894 A056635 A163116
Adjacent sequences: A166941 A166942 A166943 * A166945 A166946 A166947
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev, Oct 24 2009
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EXTENSIONS
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I corrected the terms beginning a(18) Vladimir Shevelev, Nov 10 2009
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STATUS
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approved
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