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 A259503 Numbers k such that k^2+1 is the product of a Fibonacci number and a Lucas number. 1
 0, 1, 2, 3, 5, 12, 133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Conjecture: the sequence is finite. No more terms below 25*10^4. - Robert G. Wilson v, Jul 06 2015 No more terms below 10^7. - Manfred Scheucher, Aug 03 2015 LINKS Table of n, a(n) for n=1..7. Manfred Scheucher, Sage Script EXAMPLE 0^2+1 = 1 = 1*1 = F(1)*L(1); 1^2+1 = 2 = 2*1 = F(3)*L(1); 2^2+1 = 5 = 5*1 = F(5)*L(1); 3^2+1 = 10 = 5*2 = F(5)*L(0); 5^2+1 = 26 = 13*2 = F(7)*L(0); 12^2+1 = 145 = 5*29 = F(5)*L(7); 133^2+1 = 17690 = 610*29 = F(15)*L(7). MAPLE with(combinat, fibonacci):nn:=200:lst:={}: a:=n->2*fibonacci(n-1)+fibonacci(n): for i from 0 to nn do: for j from 0 to nn do: x:=sqrt(a(i)*fibonacci(j)-1): if x=floor(x) then lst:=lst union {x}: else fi: od: od: print(lst): MATHEMATICA fibQ[n_] := (Fibonacci@ Round@ Log[ GoldenRatio, n*Sqrt@ 5 == n); fQ[n_] := Block[{k = 0, l}, While[l = LucasL@ k; l < n^2 + 2 && ! fibQ[(n^2 + 1)/l], k++]; If[l < 2 + n^2, True, False]]; k = 0; lst = {}; While[k < 250001, If[ fQ@ k, AppendTo[lst, k]; Print[k]]; k++]; lst (* Robert G. Wilson v, Jul 06 2015 *) CROSSREFS Cf. A000032, A000045, A002522. Sequence in context: A301929 A107475 A108225 * A193064 A133832 A328997 Adjacent sequences: A259500 A259501 A259502 * A259504 A259505 A259506 KEYWORD nonn,more AUTHOR Michel Lagneau, Jun 29 2015 STATUS approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)