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A304437 Least x > 0 such that x^2 + y^2 = N^N for some y > 0 and N = A230486(n) (= those N having such a solution).

%I A304437 #10 May 15 2023 12:15:33
%S A304437 10,7584,3198598,1240110271,776601600000,5917593031349125,
%T A304437 20762422068404224,62654932136711087245,1088221106880000000000,
%U A304437 1589976606572135812562944,387094246891633853991317879,6160133339397357294397161472000,12456283074641193962390812908965,441379799993599287569478479003906250
%N A304437 Least x > 0 such that x^2 + y^2 = N^N for some y > 0 and N = A230486(n) (= those N having such a solution).
%C A304437 Sequence A230486 lists those N such that N^N is the sum of two nonzero squares. Here we list the smallest x which yields such a solution x^2 + y^2 = N^N, thus necessarily y >= x.
%e A304437 See Examples in A230486.
%o A304437 (PARI) for( n=1,199, if( t=sum2sqr(n^n), t[1][0]||(t=t[^1])||next;print1(t[1][1]","))) \\ See A133388 for sum2sqr().
%o A304437 (Python)
%o A304437 from itertools import count, islice
%o A304437 from sympy import primefactors
%o A304437 from sympy.solvers.diophantine.diophantine import diop_DN
%o A304437 def A304437_gen(startvalue=2): # generator of terms
%o A304437     return map(lambda n:min(min(a,b) for a, b in diop_DN(-1,n**n) if a>0 and b>0), filter(lambda n:all(p&3==1 for p in primefactors(n)) if n&1 else any(p&3==1 for p in primefactors(n)),count(max(startvalue,2))))
%o A304437 A304437_list = list(islice(A304437_gen(),20)) # _Chai Wah Wu_, May 15 2023
%Y A304437 Cf. A230486, A000312, A000404.
%K A304437 nonn
%O A304437 1,1
%A A304437 _M. F. Hasler_ (following an idea from _Jacques Tramu_), Sep 02 2018