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URL: https://oeis.org/A139759

⇱ A139759 - OEIS

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A139759
A Fibonacci-based recurrence.
1
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
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
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