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A047621
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Numbers that are congruent to {3, 5} mod 8.
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19
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3, 5, 11, 13, 19, 21, 27, 29, 35, 37, 43, 45, 51, 53, 59, 61, 67, 69, 75, 77, 83, 85, 91, 93, 99, 101, 107, 109, 115, 117, 123, 125, 131, 133, 139, 141, 147, 149, 155, 157, 163, 165, 171, 173, 179, 181, 187, 189, 195, 197, 203, 205, 211, 213, 219, 221, 227, 229
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OFFSET
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1,1
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COMMENTS
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Numbers k for which Jacobi symbol J(2,k) = -1, so 2 (as well as 2^k) is not a square mod k. - Antti Karttunen, Aug 27 2005, corrected by Jianing Song, Nov 05 2019, see also A329095.
Numbers n whose multiplicative order modulo 2^k is 2^(k - 2) for k >= 4. For k = 3, the numbers whose multiplicative order modulo 8 is 2 are in sequence A047484. - Jianing Song, Apr 29 2018
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LINKS
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FORMULA
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G.f.: x*(3 + 2*x + 3*x^2) / ( (1 + x)*(x - 1)^2 ). - R. J. Mathar, Oct 08 2011
a(n) = 8*floor((n - 1)/2) + 4 + (-1)^n. - Gary Detlefs, Dec 03 2018
a(n) = 4*n - 2 - (-1)^n.
E.g.f.: 3 - (2 - 4*x)*exp(x) - exp(-x). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)-1)*Pi/8. - Amiram Eldar, Dec 11 2021
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MATHEMATICA
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PROG
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(Haskell)
a047621 n = a047621_list !! (n-1)
a047621_list = 3 : 5 : map (+ 8) a047621_list
(GAP) a:=[3];; for n in [2..60] do a[n]:=8*n-a[n-1]-8; od; a; # Muniru A Asiru, Dec 04 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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