A081952 - OEIS

%I #20 Jun 24 2023 04:20:38

%S 3,13,55,1597,17711,1346269,165580141,2971215073,7778742049,

%T 308061521170129,308061521170129,135301852344706746049,

%U 3311648143516982017180081,1983924214061919432247806074196061

%N Smallest Fibonacci number which is one more than the product of n distinct numbers > 1.

%H Amiram Eldar, <a href="/A081952/b081952.txt">Table of n, a(n) for n = 1..56</a>

%F a(n) = A000045(A119249(n)). - _R. J. Mathar_, Feb 06 2010

%e a(3) = 2*3*9 + 1 = 55;

%e a(4) = 3*4*7*19 + 1 = 1597;

%e a(5) = 2*5*7*11*23 + 1 = 17711;

%e a(6) = 3*4*7*11*31*47 + 1 = 1346269;

%e a(7) = 3*4*5*11*29*41*211 + 1 = 165580141;

%e a(8) = 2*3*6*7*8*23*139*461 + 1 = 2971215073.

%t f[n_, m_, 0] := n == 1; f[n_, m_, d_] := (b = False; l = Select[Divisors[n], #>=m&]; For[i = 1, i <= Length[l], i++, k = l[[i]]; If[f[n / k, k + 1, d - 1], b = True; Break[]]]; b); Do[x = 3; While[ !f[Fibonacci[x] - 1, 2, y], x++ ]; Print[Fibonacci[x]], {y, 1, 50}] (* _Ryan Propper_, Jul 22 2006 *)

%Y Subset of A000045.

%Y Cf. A000071, A081953, A119249.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Apr 02 2003

%E More terms from _R. J. Mathar_, Apr 13 2006

%E More terms from _Ryan Propper_, Jul 22 2006

%E Edited by _Jon E. Schoenfield_, Nov 18 2018