OFFSET
1,4
COMMENTS
Motivated by the fact that the first terms are zero (which is of course a coincidence). Other values (17, 65, 145, 257...) occur much more frequently.
Conjecture: a(n) = A082073(n)^2 + 1 for all n > 159. - Charles R Greathouse IV, May 13 2012
LINKS
K. Rose, Law of small numbers, primenumbers group, May 2012.
EXAMPLE
5^2+1 = 2*13, 13^2+1 = 10*17, 17^2=10*29; therefore a(1)=a(2)=a(3)=0.
29^2+1 = 22*37+28, therefore a(4)=28.
Kermit Rose's post in the primenumbers Yahoo group:
>>> (5**2+1)%13
0
>>> (13**2+1)%17
0
>>> (17**2+1)%29
0
Looks remarkable.
>>> (29**2+1)%37
28.
Oops: Break in the pattern. Another illustration of the law of small numbers. :)
PROG
(PARI) o=5; forprime(p=o+1, 900, p%4==1||next; print1((o^2+1)%o=p", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 13 2012
STATUS
approved