A212279 A002144(n+1)^2+1 mod A002144(n), where A002144 are the Pythagorean primes (p=4k+1).

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

Offset: 1

Author

M. F. Hasler, May 13 2012

Keywords

• nonn

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

Examples

			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. :)
		

Links

• K. Rose, Law of small numbers, primenumbers group, May 2012.

Programs

PARI

o=5;forprime(p=o+1,900,p%4==1||next;print1((o^2+1)%o=p","))