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A339758
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a(n) is the least prime p such that p^(2*n+1) == 2*n+1 (mod 2^(2*n+1)).
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1
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3, 3, 53, 503, 4297, 947, 10589, 17903, 624401, 7151083, 45543077, 30611047, 612126937, 2280521251, 649288301, 26566080479, 28921314337, 303937208923, 1086758949557, 12299159511127, 39118361784041, 18314722943123, 64249761922429, 2484777068103119, 1148475719438129, 14810825716436683
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OFFSET
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0,1
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LINKS
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EXAMPLE
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For n = 2, 2*n+1 = 5, and 53 is the least prime q such that q^5 == 5 (mod 2^5), so a(2) = 53.
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MAPLE
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f:= proc(k) local x, m;
for m from subs(msolve(x^k=k, 2^k), x) by 2^k do
if isprime(m) then return m fi
od
end proc:
seq(f(2*i+1), i=0..50);
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PROG
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(PARI) a(n) = my(p=2); while (Mod(p, 2^(2*n+1))^(2*n+1) != 2*n+1, p = nextprime(p+1)); p; \\ Michel Marcus, Dec 16 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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