A139759 A Fibonacci-based recurrence.

1, 1, 2, 3, 4, 7, 10, 11, 20, 31, 42, 73, 110, 183, 292, 473, 762, 1235, 1992, 3209, 5198, 8407, 13604, 22011, 35614, 57625, 93238, 150863, 244100, 394963, 639054, 1034017, 1673070, 2707089, 4380158, 7087241, 11467398, 18554639, 30022036, 48576675

Offset

0,3

Links

Table of n, a(n) for n=0..39.

E. S. Rowland, A natural prime-generating recurrence, arXiv:0710.3217 [math.NT]

Formula

a(n) = a(n-1) + a(n-2) + gcd(n,a(n-1)) - gcd(n,a(n-2)).

a(n) ~ c * phi^n, where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio and c = 0.3434866160389779937344617212678945874922532000472607933856634329169... - Vaclav Kotesovec, Dec 03 2017

Maple

A139759 := proc(n) option remember ; if n <= 1 then 1; else an_1 := A139759(n-1) ; an_2 := A139759(n-2) ; an_1+an_2+gcd(n, an_1)-gcd(n, an_2) ; fi ; end: seq(A139759(n), n=0..60) ; # R. J. Mathar, May 20 2008

Mathematica

a[0]=a[1]=1; a[n_] := a[n] = a[n-1]+a[n-2]+GCD[n, a[n-1]] - GCD[n, a[n-2]];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Dec 03 2017 *)

Crossrefs

Cf. A000045.

Sequence in context: A342790 A347873 A366567 * A030292 A204231 A135419

Adjacent sequences: A139756 A139757 A139758 * A139760 A139761 A139762

Keyword

easy,nonn

Author

Ctibor O. Zizka, May 20 2008

Extensions

More terms from R. J. Mathar, May 20 2008

Converted reference to link - R. J. Mathar, Oct 30 2009

Status

approved