A299144 a(n) is the least i such that gcd(Fibonacci(i), i+x) > 1 for all x=0..n.

5, 10, 18, 30, 30, 30, 30, 180, 180, 180, 180, 840, 840, 1260, 1260, 1260, 1260, 24480, 24480, 63000, 63000, 63000, 63000, 63000, 63000, 63000, 63000, 63000, 63000, 356400, 356400, 356400, 356400, 356400, 356400, 356400, 356400, 5783400, 5783400, 5783400, 5783400, 5783400, 5783400

Offset: 0

Author

Alex Ratushnyak, Feb 03 2018

Keywords

• nonn

Examples

			5 is the smallest integer i such that gcd(F(i), i) > 1, because F(5)=5. Therefore a(0)=5.
10 is the smallest integer i such that gcd(F(i), i) > 1 and gcd(F(i), i+1) > 1, because F(10)=55, not coprime to 10 nor 11. Therefore a(1)=10.
		

Crossrefs

Cf. A000045, A104714.

Programs

Mathematica

Nest[Function[a, Append[a, SelectFirst[Range[10^5], Function[i, AllTrue[i + Range[0, Length@ a], ! CoprimeQ[Fibonacci@ i, #] &]]]]], {}, 29] (* Michael De Vlieger, Feb 05 2018 *)

PARI

isok(k, n) = {for (x=0, n, if (gcd(fibonacci(k), k+x) == 1, return(0));); return(1);}
a(n) = {my(k=1); while (!isok(k,n), k++); k;} \\ Michel Marcus, Feb 05 2018

Python

p0=0
p1=1
def GCD(x,y):
    tmp = y
    y = x % y
    if y==0: return tmp
    return GCD(tmp, y)
n=0
for i in range(1,1000000):
    p0,p1 = p1, p0+p1
    for x in range(1000000):
        if GCD(p0,i+x)==1: break
    for j in range(n, x):
        print(i)
    if x>n: n=x

Extensions

a(29)-a(36) from Michael De Vlieger, Feb 05 2018

a(37)-a(42) from Jon E. Schoenfield, Apr 24 2018