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A350540
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a(n) = smallest number x such that x^2 == 17 (mod 2^n).
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1
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0, 1, 1, 1, 1, 7, 9, 23, 23, 23, 233, 279, 279, 1769, 1769, 6423, 9961, 9961, 55575, 55575, 206569, 206569, 842007, 1255145, 2939159, 2939159, 2939159, 2939159, 64169705, 64169705, 204265751, 204265751, 869476073, 869476073, 3425491223, 3425491223, 13754377961
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OFFSET
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0,6
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COMMENTS
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17 is the smallest nonsquare that is congruent to a square mod 2^n for any n.
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.
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LINKS
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MATHEMATICA
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PROG
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(PARI) a(n) = my(x=0); while (Mod(x, 2^n)^2 != 17, x++); x; \\ Michel Marcus, Jan 04 2022
(Python)
from sympy.ntheory import sqrt_mod
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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