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A350540 a(n) = smallest number x such that x^2 == 17 (mod 2^n).

%I A350540 #39 Feb 03 2023 15:25:20
%S A350540 0,1,1,1,1,7,9,23,23,23,233,279,279,1769,1769,6423,9961,9961,55575,
%T A350540 55575,206569,206569,842007,1255145,2939159,2939159,2939159,2939159,
%U A350540 64169705,64169705,204265751,204265751,869476073,869476073,3425491223,3425491223,13754377961
%N A350540 a(n) = smallest number x such that x^2 == 17 (mod 2^n).
%C A350540 17 is the smallest nonsquare that is congruent to a square mod 2^n for any n.
%C A350540 Any number that is congruent to a square mod 2^n for any n is of the form (4^a)*(8b+1). Such numbers have density 1/6.
%H A350540 Chai Wah Wu, <a href="/A350540/b350540.txt">Table of n, a(n) for n = 0..1000</a>
%t A350540 Table[PowerMod[17,1/2,2^k],{k,0,36}] (* _Giorgos Kalogeropoulos_, Jan 31 2023 *)
%o A350540 (PARI) a(n) = my(x=0); while (Mod(x, 2^n)^2 != 17, x++); x; \\ _Michel Marcus_, Jan 04 2022
%o A350540 (Python)
%o A350540 from sympy.ntheory import sqrt_mod
%o A350540 def A350540(n): return min(sqrt_mod(17,2**n,all_roots=True)) # _Chai Wah Wu_, Jan 12 2022
%Y A350540 Cf. A000290, A000079.
%K A350540 nonn
%O A350540 0,6
%A A350540 _Tejo Vrush_, Jan 04 2022
%E A350540 a(13)-a(28) from _Michel Marcus_, Jan 04 2022
%E A350540 a(30)-a(36) from _Alois P. Heinz_, Jan 04 2022
%E A350540 Edited by _N. J. A. Sloane_, Jan 12 2022