



0, 0, 0, 28, 17, 39, 4, 72, 79, 65, 17, 65, 17, 29, 145, 65, 84, 65, 145, 17, 109, 17, 65, 0, 145, 65, 17, 145, 88, 17, 64, 145, 17, 28, 257, 65, 17, 65, 145, 145, 257, 65, 17, 269, 145, 401, 257, 145, 65, 257, 65, 145, 17, 577, 145, 65, 145, 17, 577, 65, 577
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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

Table of n, a(n) for n=1..61.
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==1next; print1((o^2+1)%o=p", "))


CROSSREFS

Sequence in context: A033970 A033348 A040759 * A040758 A196031 A196028
Adjacent sequences: A212276 A212277 A212278 * A212280 A212281 A212282


KEYWORD

nonn


AUTHOR

M. F. Hasler, May 13 2012


STATUS

approved



