This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047621 #63 Nov 22 2024 09:06:45
%S A047621 3,5,11,13,19,21,27,29,35,37,43,45,51,53,59,61,67,69,75,77,83,85,91,
%T A047621 93,99,101,107,109,115,117,123,125,131,133,139,141,147,149,155,157,
%U A047621 163,165,171,173,179,181,187,189,195,197,203,205,211,213,219,221,227,229
%N A047621 Numbers that are congruent to {3, 5} mod 8.
%C A047621 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.
%C A047621 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
%H A047621 Muniru A Asiru, <a href="/A047621/b047621.txt">Table of n, a(n) for n = 1..5000</a>
%H A047621 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047621 a(n) = 8*n - a(n-1) - 8 (with a(1) = 3). - _Vincenzo Librandi_, Aug 06 2010
%F A047621 G.f.: x*(3 + 2*x + 3*x^2) / ( (1 + x)*(x - 1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F A047621 A089911(3*a(n)) = 10. - _Reinhard Zumkeller_, Jul 05 2013
%F A047621 a(n) = 8*floor((n - 1)/2) + 4 + (-1)^n. - _Gary Detlefs_, Dec 03 2018
%F A047621 From _Franck Maminirina Ramaharo_, Dec 03 2018: (Start)
%F A047621 a(n) = 4*n - 2 - (-1)^n.
%F A047621 E.g.f.: 3 - (2 - 4*x)*exp(x) - exp(-x). (End)
%F A047621 a(n + 2) = a(n) + 8. - _David A. Corneth_, Dec 03 2018
%F A047621 Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)-1)*Pi/8. - _Amiram Eldar_, Dec 11 2021
%F A047621 From _Amiram Eldar_, Nov 22 2024: (Start)
%F A047621 Product_{n>=1} (1 - (-1)^n/a(n)) = sec(Pi/8) (1/A144981).
%F A047621 Product_{n>=1} (1 + (-1)^n/a(n)) = 2*sin(Pi/8) (A101464). (End)
%t A047621 LinearRecurrence[{1, 1, -1}, {3, 5, 11}, 100] (* _Jean-François Alcover_, Jul 31 2018 *)
%o A047621 (Haskell)
%o A047621 a047621 n = a047621_list !! (n-1)
%o A047621 a047621_list = 3 : 5 : map (+ 8) a047621_list
%o A047621 -- _Reinhard Zumkeller_, Jul 05 2013
%o A047621 (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
%Y A047621 Row 1 of A112070. Complement of A047522 relative to A005408. Primes in this sequence: A003629.
%Y A047621 Subsequence of A329095.
%Y A047621 Cf. A047522, A066507, A101464, A144981.
%K A047621 nonn,easy
%O A047621 1,1
%A A047621 _N. J. A. Sloane_