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A187715
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a(n) = 5*n - (9 + (-1)^n)/2.
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1
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1, 5, 11, 15, 21, 25, 31, 35, 41, 45, 51, 55, 61, 65, 71, 75, 81, 85, 91, 95, 101, 105, 111, 115, 121, 125, 131, 135, 141, 145, 151, 155, 161, 165, 171, 175, 181, 185, 191, 195, 201, 205, 211, 215, 221, 225
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = a(n-1) + 4 if n is even, a(n) = a(n-1) + 6 if n is odd.
a(n) = 2*a(n-1) - a(n-2) - 2*(-1)^n.
G.f.: x*(1 + 4*x + 5*x^2)/( (1+x)*(1-x)^2 ).
a(n) = 5*(n-1) bitwise-OR 1. - Jon Maiga, Nov 24 2018
E.g.f.: ((10*x-9)*exp(x) - exp(-x) + 10)/2. - G. C. Greubel, Dec 04 2018
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
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MAPLE
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MATHEMATICA
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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 *)
Table[BitOr[5*n, 1], {n, 0, 50}] (* Jon Maiga, Nov 24 2018 *)
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PROG
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(Magma) [5*n -(9+(-1)^n)/2: n in [1..60]];
(GAP) Filtered([1..250], n-> n mod 10 =1 or n mod 10 = 5); # Muniru A Asiru, Nov 25 2018
(Python) for n in range(1, 60): print(int(5*n - (9 + (-1)**n)/2), end=', ') # Stefano Spezia, Nov 30 2018
(PARI) vector(50, n, (10*n -9-(-1)^n)/2) \\ G. C. Greubel, Dec 04 2018
(Sage) [(10*n -9-(-1)^n)/2 for n in (1..50)] # G. C. Greubel, 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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EXTENSIONS
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STATUS
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approved
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