A166944 a(1)=2; a(n) = a(n-1) + gcd(n, a(n-1)) if n is even, a(n) = a(n-1) + gcd(n-2, a(n-1)) if n is odd.

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

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

Cf. A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293.

Sequence in context: A125881 A287370 A089969 * A073894 A341496 A056635

Adjacent sequences: A166941 A166942 A166943 * A166945 A166946 A166947

Keyword

nonn

Author

Vladimir Shevelev, Oct 24 2009

Extensions

Terms beginning with a(18) corrected by Vladimir Shevelev, Nov 10 2009

Status

approved