cp's OEIS Frontend

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

%I A059321 #11 May 04 2024 02:54:37
%S A059321 7,70,38,41,117,378,500,682,776,3861,4052,515,5744,1710,6613,1744,
%T A059321 11018,13241,3458,5099,1393,16610,26884,15006,2072,13637,31361,4443,
%U A059321 26508,7850,37520,31152,39922,37107,6072,4005,32491,4030,43211,12238
%N A059321 Smallest number m such that m^2+1 is divisible by A002144(n)^2 (= squares of primes congruent to 1 mod 4).
%C A059321 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.
%H A059321 Chai Wah Wu, <a href="/A059321/b059321.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2000 from Klaus Brockhaus)
%o A059321 (Python)
%o A059321 from itertools import islice
%o A059321 from sympy import nextprime, sqrt_mod_iter
%o A059321 def A059321_gen(): # generator of terms
%o A059321     p = 1
%o A059321     while (p:=nextprime(p)):
%o A059321         if p&3==1:
%o A059321             yield min(sqrt_mod_iter(-1,p**2))
%o A059321 A059321_list = list(islice(A059321_gen(),20)) # _Chai Wah Wu_, May 04 2024
%Y A059321 Cf. A002144, A059591, A059592.
%K A059321 easy,nonn
%O A059321 1,1
%A A059321 _Marc LeBrun_, Jan 26 2001