|
|
A215938
|
|
Numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 5*b^2.
|
|
1
|
|
|
1, 2, 5, 8, 11, 12, 25, 29, 32, 41, 48, 55, 89, 121, 125, 128, 131, 145, 179, 192, 205, 275, 331, 359, 401, 421, 431, 445, 449, 509, 512, 569, 571, 601, 605, 625, 631, 655, 659, 691, 725, 768, 895, 911, 1025, 1375
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
A number n can be written in the form a^2+5*b^2 if and only if n is 0, or of the form 2^(2i) 5^j Prod_{p==1 or 9 mod 20} p^k Prod_{q==3 or 7 mod 20) q^(2m) or of the form 2^(2i+1) 5^j Prod_{p==1 or 9 mod 20} p^k Prod_{q==3 or 7 mod 20) q^(2m+1), for integers i,j,k,m, for primes p,q.
|
|
LINKS
|
|
|
PROG
|
(PARI) for(i=2, 500, a=factorint(fibonacci(i))~; flag=0; flip=0; for(j=1, #a, if(((a[1, j]%20>10))&&a[2, j]%2==1, flag=1); if(((a[1, j]%20==2)||(a[1, j]%20==3)||(a[1, j]%20==7))&&a[2, j]%2==1, flip=flip+1)); if(flag==0&&flip%2==0, print(i", ")))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Terms corrected by V. Raman, Sep 20 2012
|
|
STATUS
|
approved
|
|
|
|