This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A145298 #8 May 04 2024 02:55:12
%S A145298 1068,143044,390112,7745569,6423465,46464143,23048345,144762466,
%T A145298 404034898,2153335831,331407850,1108900220,2581164875,760839155,
%U A145298 10734466938,6595297216,773302059,61063137802,31915893786,112699451831
%N A145298 Smallest k such that k^2+1 is divisible by A002144(n)^5.
%H A145298 Chai Wah Wu, <a href="/A145298/b145298.txt">Table of n, a(n) for n = 1..10000</a>
%e A145298 a(4) = 7745569 since A002144(4) = 29, 7745569^2+1 = 59993839133762 = 2*29^5*97*15077 and for no k < 7745569 does 29^5 divide k^2+1.
%o A145298 (PARI) {e=5; forprime(p=2, 200, if(p%4==1, q=p^e; m=q; while(!ispower(m-1,2,&n), m=m+q); print1(n, ",")))}
%o A145298 (Python)
%o A145298 from itertools import islice
%o A145298 from sympy import nextprime, sqrt_mod_iter
%o A145298 def A145298_gen(): # generator of terms
%o A145298 p = 1
%o A145298 while (p:=nextprime(p)):
%o A145298 if p&3==1:
%o A145298 yield min(sqrt_mod_iter(-1,p**5))
%o A145298 A145298_list = list(islice(A145298_gen(),20)) # _Chai Wah Wu_, May 04 2024
%Y A145298 Cf. A002144 (primes of form 4n+1), A002313 (-1 is a square mod p), A059321, A145296, A145297, A145299.
%K A145298 nonn
%O A145298 1,1
%A A145298 _Klaus Brockhaus_, Oct 14 2008