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 A212279 A002144(n+1)^2+1 mod A002144(n), where A002144 are the Pythagorean primes (p=4k+1). 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified October 28 21:20 EDT 2020. Contains 338064 sequences. (Running on oeis4.)