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Indices of Fibonacci numbers in A081952.
1

%I #9 Jun 24 2023 04:21:28

%S 4,7,10,17,22,31,41,47,49,71,71,98,119,161,169,191,191,239,239,239,

%T 338,338,338,431,431,449,529,599,649,649,769,769,769,769,769,769,1009,

%U 1009,1009,1409,1441,1441,1441,1441,1729,1889,1889,1889,1889,2159,2209,2209,2209,2591,2642,2642

%N Indices of Fibonacci numbers in A081952.

%F A081952(n) = F(a(n)), where F(k) is the k-th Fibonacci number.

%F a(n) = the smallest k>3 such that A086435(A000045(k)-1)>=n. - _Max Alekseyev_, Apr 23 2010

%e A081952(4) = 1597 and 1597 is the 17th Fibonacci number, so a(4) = 17.

%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[x], {y, 1, 50}]

%Y Cf. A000045, A000071, A081952, A086435.

%K nonn

%O 1,1

%A _Ryan Propper_, Jul 22 2006

%E a(24)-a(26) from _Max Alekseyev_, Apr 23 2010

%E a(27)-a(56) from _Amiram Eldar_, Jun 24 2023