A059321 Smallest number m such that m^2+1 is divisible by A002144(n)^2 (= squares of primes congruent to 1 mod 4).

7, 70, 38, 41, 117, 378, 500, 682, 776, 3861, 4052, 515, 5744, 1710, 6613, 1744, 11018, 13241, 3458, 5099, 1393, 16610, 26884, 15006, 2072, 13637, 31361, 4443, 26508, 7850, 37520, 31152, 39922, 37107, 6072, 4005, 32491, 4030, 43211, 12238

Offset: 1

Author

Marc LeBrun, Jan 26 2001

Keywords

• easy
• nonn

Comments

a(2) = 70 since A002144(2)=13, 70^2+1 = 4091 = 13^2 * 29 and for no k<70 does 13^2 divide k^2+1. Related to period-1 continued fractions.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Klaus Brockhaus)

Crossrefs

Cf. A002144, A059591, A059592.

Programs

Python

from itertools import islice
from sympy import nextprime, sqrt_mod_iter
def A059321_gen(): # generator of terms
    p = 1
    while (p:=nextprime(p)):
        if p&3==1:
            yield min(sqrt_mod_iter(-1,p**2))
A059321_list = list(islice(A059321_gen(),20)) # Chai Wah Wu, May 04 2024