A214646 a(n) = (a(n-2) + a(n-3))/gcd(a(n-2), a(n-3)) with a(1) = a(2) = a(3) = 1.

1, 1, 1, 2, 2, 3, 2, 5, 5, 7, 2, 12, 9, 7, 7, 16, 2, 23, 9, 25, 32, 34, 57, 33, 91, 30, 124, 121, 77, 245, 18, 46, 263, 32, 309, 295, 341, 604, 636, 945, 310, 527, 251, 27, 778, 278, 805, 528, 1083, 1333, 537, 2416, 1870, 2953, 2143, 4823, 5096, 6966, 109

Offset

1,4

Comments

A variation on A214551 with the second and third terms being added and divided by the greatest common divisor of the pair of numbers.

Links

Reed Kelly, Table of n, a(n) for n = 1..1003

Example

a(6) = (a(4)+a(3))/gcd(a(4),a(3)) = (2+1)/1 = 3.
a(19) = (a(17)+a(16))/gcd(a(17),a(16)) = (2+16)/2 = 9.

Mathematica

DivGCDxy[n_, x_, y_, init_] := Module[{t, a, i}, t = init;
  Do[AppendTo[t, (t[[-x]] + t[[-y]])/GCD[t[[-x]], t[[-y]]]], {n}];
  t]; DivGCDxy[100, 2, 3, {1, 1, 1}]

Crossrefs

Cf. A214551, A000931.

Sequence in context: A254858 A050323 A318286 * A340693 A275382 A378747

Adjacent sequences: A214643 A214644 A214645 * A214647 A214648 A214649

Keyword

nonn

Author

Reed Kelly, Jul 24 2012

Extensions

NAME adapted to offset and b-file. - R. J. Mathar, Jun 19 2021

Status

approved