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A047621 Numbers that are congruent to {3, 5} mod 8. 19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
a(n) = 8*n - a(n-1) - 8 (with a(1) = 3). - Vincenzo Librandi, Aug 06 2010
G.f.: x*(3 + 2*x + 3*x^2) / ( (1 + x)*(x - 1)^2 ). - R. J. Mathar, Oct 08 2011
A089911(3*a(n)) = 10. - Reinhard Zumkeller, Jul 05 2013
a(n) = 8*floor((n - 1)/2) + 4 + (-1)^n. - Gary Detlefs, Dec 03 2018
From Franck Maminirina Ramaharo, Dec 03 2018: (Start)
a(n) = 4*n - 2 - (-1)^n.
E.g.f.: 3 - (2 - 4*x)*exp(x) - exp(-x). (End)
a(n + 2) = a(n) + 8. - David A. Corneth, Dec 03 2018
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)-1)*Pi/8. - Amiram Eldar, Dec 11 2021
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {3, 5, 11}, 100] (* Jean-François Alcover, Jul 31 2018 *)
PROG
(Haskell)
a047621 n = a047621_list !! (n-1)
a047621_list = 3 : 5 : map (+ 8) a047621_list
-- Reinhard Zumkeller, Jul 05 2013
(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
CROSSREFS
Row 1 of A112070. Complement of A047522 relative to A005408. Primes in this sequence: A003629.
Subsequence of A329095.
Cf. A066507.
Cf. A047522.
Sequence in context: A153443 A211876 A066587 * A239636 A117205 A147992
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)