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A166944 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 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture. Every record of differences a(n)-a(n-1) more than 5 is greater of twin primes (A006512)

REFERENCES

E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol.11(2008), Article 08.2.8

LINKS

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]

MAPLE

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Oct 24 2009

EXTENSIONS

I corrected the terms beginning a(18) Vladimir Shevelev, Nov 10 2009

STATUS

approved

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Last modified November 22 22:27 EST 2014. Contains 249835 sequences.