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A187715 a(n) = 5*n - (9 + (-1)^n)/2.

%I A187715 #45 Apr 15 2023 04:19:34
%S A187715 1,5,11,15,21,25,31,35,41,45,51,55,61,65,71,75,81,85,91,95,101,105,
%T A187715 111,115,121,125,131,135,141,145,151,155,161,165,171,175,181,185,191,
%U A187715 195,201,205,211,215,221,225
%N A187715 a(n) = 5*n - (9 + (-1)^n)/2.
%C A187715 Numbers congruent to {1,5} mod 10. - _Bruno Berselli_, Mar 31 2012
%H A187715 Vincenzo Librandi, <a href="/A187715/b187715.txt">Table of n, a(n) for n = 1..10000</a>
%H A187715 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A187715 a(n) = a(n-1) + 4 if n is even, a(n) = a(n-1) + 6 if n is odd.
%F A187715 a(n) = 2*a(n-1) - a(n-2) - 2*(-1)^n.
%F A187715 From _R. J. Mathar_, Mar 15 2011: (Start)
%F A187715 G.f.: x*(1 + 4*x + 5*x^2)/( (1+x)*(1-x)^2 ).
%F A187715 Bisections: a(2*n+1) = A017281(n), a(2*n) = A017329(n-1). (End)
%F A187715 a(n) = 5*(n-1) bitwise-OR 1. - _Jon Maiga_, Nov 24 2018
%F A187715 E.g.f.: ((10*x-9)*exp(x) - exp(-x) + 10)/2. - _G. C. Greubel_, Dec 04 2018
%F A187715 Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(5+2*sqrt(5))*Pi/20 + 3*log(phi)/(4*sqrt(5)) + log(5)/8, where phi is the golden ratio (A001622). - _Amiram Eldar_, Apr 15 2023
%p A187715 [5*n-(9+(-1)^n)/2$n=1..50]; # _Muniru A Asiru_, Nov 25 2018
%t A187715 nxt[{n_,a_}]:={n+1,If[EvenQ[n+1],a+4,a+6]}; Transpose[NestList[nxt,{1,1},50]][[2]] (* _Harvey P. Dale_, Feb 16 2013 *)
%t A187715 Table[BitOr[5*n, 1], {n, 0, 50}] (* _Jon Maiga_, Nov 24 2018 *)
%o A187715 (Magma) [5*n -(9+(-1)^n)/2: n in [1..60]];
%o A187715 (GAP) Filtered([1..250],n-> n mod 10 =1 or n mod 10 = 5); # _Muniru A Asiru_, Nov 25 2018
%o A187715 (Python) for n in range(1,60): print(int(5*n - (9 + (-1)**n)/2), end=', ') # _Stefano Spezia_, Nov 30 2018
%o A187715 (PARI) vector(50, n, (10*n -9-(-1)^n)/2) \\ _G. C. Greubel_, Dec 04 2018
%o A187715 (Sage) [(10*n -9-(-1)^n)/2 for n in (1..50)] # _G. C. Greubel_, Dec 04 2018
%Y A187715 Cf. A001622, A010711 (first differences), A017281, A017329.
%K A187715 nonn,easy
%O A187715 1,2
%A A187715 _Vincenzo Librandi_, Mar 13 2011
%E A187715 Definition rewritten by _R. J. Mathar_, Mar 15 2011