A178777 -id:A178777 - cp's OEIS frontend

A201010 Integers that can be written as the product and/or quotient of Lucas numbers.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 23, 24, 27, 28, 29, 31, 32, 33, 36, 38, 41, 42, 44, 46, 47, 48, 49, 54, 56, 57, 58, 62, 63, 64, 66, 69, 72, 76, 77, 81, 82, 84, 87, 88, 92, 93, 94, 96, 98, 99, 107, 108, 112, 114, 116, 121, 123, 124, 126, 128

Offset: 1

Arkadiusz Wesolowski, Jan 08 2013

These numbers do not occur in A178777.
The first 20 terms of this sequence are the same as in A004144 (nonhypotenuse numbers).
Integers of the form A200381(n)/A200381(m) for some m and n.

			19 is in the sequence because Lucas(9)/Lucas(0)^2 = 19.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Lucas Number
Index entries for Lucas sequences

Cf. A000032, A200381, A200995, A201011. Subsequence of A178772. Complement of A201012.

maxTerm = 128; Clear[f]; f[lim_] := f[lim] = (luc = LucasL[Range[0, lim]]; luc = Delete[luc, 2];  last = luc[[-1]]; t = {1}; Do[t2 = luc[[n]]^Range[ Floor[ Log[last] / Log[ luc[[n]] ]]]; s = Select[ Union[ Flatten[ Outer[ Times, t, t2]]], # <= last &]; t = Union[t, s], {n, lim}]; maxIndex = Length[A200381 = t]; Reap[ Do[r = A200381[[n]] / A200381[[m]]; If[IntegerQ[r] && r <= maxTerm, Sow[r]], {n, 1, maxIndex}, {m, 1, maxIndex}]][[2, 1]] // Union); f[5]; f[lim = 10]; While[ Print["lim = ", lim]; f[lim] != f[lim-5], lim = lim+5]; f[lim] (* Jean-François Alcover, Jun 24 2015, after script by T. D. Noe in A200381 *)

A185060 Number of Fibonacci integers in the interval [1, 10^n].

Original entry on oeis.org

10, 88, 534, 2645, 11254, 42735

Offset: 1

Arkadiusz Wesolowski, Dec 25 2012

A Fibonacci integer is an integer in the multiplicative group generated by the Fibonacci numbers. For each fixed epsilon > 0,
exp(C*(log(10^n))^1/2 - (log(10^n))^epsilon) < a(n) < exp(C*(log(10^n))^1/2 + (log(10^n))^(1/6+epsilon)) for x sufficiently large, where C = 2*zeta(2)*sqrt(zeta(3)/(zeta(6)*log((1 + sqrt(5))/2))) = 5.15512.... (Luca, Pomerance, Wagner (2010))
The old entry a(4) = 2681 was the result of an incorrect calculation by Luca, Pomerance and Wagner. - Arkadiusz Wesolowski, Feb 05 2013

Florian Luca, Carl Pomerance, and Stephen Wagner, Fibonacci integers (Banff conference in honor of Cam Stewart, May 31, 2010 to June 4, 2010.)

Cf. A178772, A178777.

e = 4; (*lst1=the terms of A178762 that are smaller than 10^e*); lst1 = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 61, 89, 107, 199, 211, 233, 281, 421, 521, 1103, 1597, 2161, 2207, 2521, 3001, 3571, 5779, 9349, 9901}; lst2 = {}; q = Times @@ Complement[Prime@Range[10^e], lst1]; Do[If[GCD[q, n] == 1, AppendTo[lst2, n]], {n, 10^e}]; Table[Length@Select[lst2, # <= 10^d &], {d, e}] (* Arkadiusz Wesolowski, Feb 05 2013 *)

a(4) corrected by T. D. Noe and Arkadiusz Wesolowski, Feb 05 2013

a(5)-a(6) from Arkadiusz Wesolowski, Feb 06 2013

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A201010 Integers that can be written as the product and/or quotient of Lucas numbers.

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