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 A047211 #71 Mar 26 2024 10:09:56
%S A047211 2,4,7,9,12,14,17,19,22,24,27,29,32,34,37,39,42,44,47,49,52,54,57,59,
%T A047211 62,64,67,69,72,74,77,79,82,84,87,89,92,94,97,99,102,104,107,109,112,
%U A047211 114,117,119,122,124,127,129,132,134,137,139,142,144,147,149,152,154,157,159,162,164,167,169,172,174,177,179,182,184
%N A047211 Numbers that are congruent to {2, 4} mod 5.
%C A047211 Conjecture: n such that the characteristic polynomial of M(n) is irreducible over the rationals where M(n) is an n X n matrix with ones on the skew diagonal and below it and the skew line two positions above it and otherwise zeros; see example for one such matrix. Tested up to n=177. - _Joerg Arndt_, Aug 10 2011
%H A047211 David Lovler, <a href="/A047211/b047211.txt">Table of n, a(n) for n = 1..1000</a>
%H A047211 Melvyn B. Nathanson, <a href="http://dx.doi.org/10.4169/amer.math.monthly.120.05.409">On the fractional parts of roots of positive real numbers</a>, Amer. Math. Monthly, Vol. 120, No. 5 (2013), pp. 409-429 [see p. 417].
%H A047211 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047211 a(n) = a(n-1) +a(n-2) -a(n-3).
%F A047211 a(n) = (10*n-3-(-1)^n)/4, (n>=1). [Corrected by _Bruno Berselli_, Sep 20 2010]
%F A047211 a(n) = 5*floor((n-1)/2) +3 +(-1)^n. - _Gary Detlefs_, Mar 02 2010
%F A047211 G.f.: x*(2+2*x+x^2)/((1+x)*(1-x)^2). - _Paul Barry_, Sep 11 2008
%F A047211 a(n) = 5*n-a(n-1)-4 (with a(1)=2). - _Vincenzo Librandi_, Nov 18 2010
%F A047211 a(n) = floor((5*n-1)/2). - _Gary Detlefs_, May 14 2011
%F A047211 a(n) = 2*n + floor((n-1)/2). - _Arkadiusz Wesolowski_, Sep 19 2012
%F A047211 Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2+2/sqrt(5))*Pi/10 - sqrt(5)*log(phi)/5, where phi is the golden ratio (A001622). - _Amiram Eldar_, Dec 07 2021
%F A047211 E.g.f.: 1 + ((10*x - 3)*exp(x) - exp(-x))/4. - _David Lovler_, Aug 23 2022
%e A047211 The 7 X 7 matrix (dots for zeros):
%e A047211 [....1.1]
%e A047211 [...1.11]
%e A047211 [..1.111]
%e A047211 [.1.1111]
%e A047211 [1.11111]
%e A047211 [.111111]
%e A047211 [1111111]
%e A047211 has the characteristic polynomial x^7 - 5*x^6 - 4*x^5 + 15*x^4 + 5*x^3 - 11*x^2 - x + 1 which is irreducible over the field of rational numbers, and 7 is a term of the sequence. - _Joerg Arndt_, Aug 10 2011
%p A047211 seq(5*floor((n-1)/2) +3 +(-1)^n, n=1..50); # _Gary Detlefs_, Mar 02 2010
%t A047211 Select[Range[0, 200], MemberQ[{2, 4}, Mod[#, 5]] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 12 2012 *)
%t A047211 LinearRecurrence[{1,1,-1},{2,4,7},80] (* _Harvey P. Dale_, Mar 26 2024 *)
%o A047211 (Haskell)
%o A047211 a047211 n = a047211_list !! (n-1)
%o A047211 a047211_list = filter ((`elem` [2,4]) . (`mod` 5)) [1..]
%o A047211 -- _Reinhard Zumkeller_, Oct 03 2012
%o A047211 (Magma) [Floor((5*n-1)/2): n in [1..50]]; // _Wesley Ivan Hurt_, May 25 2014
%o A047211 (PARI) a(n)=(5*n-1)\2 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A047211 Cf. A001622, A047209.
%Y A047211 Cf. A053685 (subsequence).
%K A047211 nonn,easy
%O A047211 1,1
%A A047211 _N. J. A. Sloane_, Dec 11 1999
%E A047211 Conjecture corrected by _John M. Campbell_, Aug 25 2011