OFFSET
1,1
COMMENTS
Conjecture: Every record of differences a(n)-a(n-1) more than 5 is the greater of twin primes (A006512).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol.11(2008), Article 08.2.8. arXiv:0710.3217 [math.NT]
V. Shevelev, An infinite set of generators of primes based on the Rowland idea and conjectures concerning twin primes, arXiv:0910.4676 [math.NT], 2009. - Vladimir Shevelev, Oct 27 2009
V. Shevelev, Three theorems on twin primes, arXiv:0911.5478 [math.NT], 2009-2010. - 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
MATHEMATICA
nxt[{n_, a_}]:={n+1, If[OddQ[n], a+GCD[n+1, a], a+GCD[n-1, a]]}; Transpose[ NestList[ nxt, {1, 2}, 70]][[2]] (* Harvey P. Dale, Feb 10 2015 *)
PROG
(PARI) print1(a=2); for(n=2, 100, d=gcd(a, if(n%2, n-2, n)); print1(", "a+=d)) \\ Charles R Greathouse IV, Oct 13 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Oct 24 2009
EXTENSIONS
Terms beginning with a(18) corrected by Vladimir Shevelev, Nov 10 2009
STATUS
approved