OFFSET
0,1
EXAMPLE
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.
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 *)
PROG
(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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Feb 03 2018
EXTENSIONS
a(29)-a(36) from Michael De Vlieger, Feb 05 2018
a(37)-a(42) from Jon E. Schoenfield, Apr 24 2018
STATUS
approved