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A145297 Smallest k such that k^2+1 is divisible by A002144(n)^4.

%I A145297 #8 May 04 2024 02:53:08
%S A145297 182,239,27493,34522,800982,1251967,623098,6304056,6459524,20099637,
%T A145297 22709274,35764191,40317977,54397650,166206108,187800003,165728858,
%U A145297 152475014,282599844,312923750,154613663,485200742,912190662,548850444
%N A145297 Smallest k such that k^2+1 is divisible by A002144(n)^4.
%H A145297 Chai Wah Wu, <a href="/A145297/b145297.txt">Table of n, a(n) for n = 1..10000</a>
%e A145297 a(1) = 182 since A002144(1) = 5, 182^2+1 = 33125 = 5^4*53 and for no k < 182 does 5^4 divide k^2+1.
%o A145297 (PARI) {e=4; forprime(p=2, 250, if(p%4==1, q=p^e; m=q; while(!ispower(m-1,2,&n), m=m+q); print1(n, ",")))}
%o A145297 (Python)
%o A145297 from itertools import islice
%o A145297 from sympy import nextprime, sqrt_mod_iter
%o A145297 def A145297_gen(): # generator of terms
%o A145297     p = 1
%o A145297     while (p:=nextprime(p)):
%o A145297         if p&3==1:
%o A145297             yield min(sqrt_mod_iter(-1,p**4))
%o A145297 A145297_list = list(islice(A145297_gen(),20)) # _Chai Wah Wu_, May 04 2024
%Y A145297 Cf. A002144 (primes of form 4n+1), A002313 (-1 is a square mod p), A059321, A145296, A145298, A145299.
%K A145297 nonn
%O A145297 1,1
%A A145297 _Klaus Brockhaus_, Oct 11 2008