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A015950
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Numbers k such that k | 4^k + 1.
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18
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1, 5, 25, 125, 205, 625, 1025, 2525, 3125, 5125, 8405, 12625, 15625, 25625, 42025, 63125, 78125, 103525, 128125, 168305, 202525, 210125, 255025, 315625, 344605, 390625, 517625, 640625, 841525, 875125, 1012625, 1050625, 1275125
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OFFSET
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1,2
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COMMENTS
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All terms except 1 are congruent to 5 mod 20.
If k is a term and prime p | k, then k*p is a term.
All prime factors of terms == 1 (mod 4).
If p is a prime == 1 (mod 4) and the order of 4 (mod p) is 2*m where m is in the sequence, then m*p is in the sequence. (End)
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LINKS
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EXAMPLE
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4^5 + 1 = 1025 and 1025 is divisible by 5, so 5 is a term.
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MAPLE
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select(n -> 4 &^ n + 1 mod n = 0, [1, seq(i, i=5..10^7, 20)]); # Robert Israel, Sep 14 2017
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MATHEMATICA
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Select[Prepend[20 Range[0, 10^5] + 5, 1], Mod[4^# + 1, #] == 0 &] (* Michael De Vlieger, Dec 31 2018 *)
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PROG
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(Magma) [n: n in [1..10^6] | Modexp(4, n, n)+1 eq n]; // Jinyuan Wang, Dec 29 2018
(Python)
A015950_list = [n for n in range(1, 10**6) if pow(4, n, n) == n-1] # Chai Wah Wu, Mar 25 2021
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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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