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).

10, 7584, 3198598, 1240110271, 776601600000, 5917593031349125, 20762422068404224, 62654932136711087245, 1088221106880000000000, 1589976606572135812562944, 387094246891633853991317879, 6160133339397357294397161472000, 12456283074641193962390812908965, 441379799993599287569478479003906250

Offset: 1

Author

M. F. Hasler (following an idea from Jacques Tramu), Sep 02 2018

Keywords

• nonn

Comments

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.

Examples

			See Examples in A230486.
		

Crossrefs

Cf. A230486, A000312, A000404.

Programs

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().

Python

from itertools import count, islice
from sympy import primefactors
from sympy.solvers.diophantine.diophantine import diop_DN
def A304437_gen(startvalue=2): # generator of terms
    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))))
A304437_list = list(islice(A304437_gen(),20)) # Chai Wah Wu, May 15 2023