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URL: https://oeis.org/A047535

⇱ A047535 - OEIS

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A047535
Numbers that are congruent to {4, 7} mod 8.
17
4, 7, 12, 15, 20, 23, 28, 31, 36, 39, 44, 47, 52, 55, 60, 63, 68, 71, 76, 79, 84, 87, 92, 95, 100, 103, 108, 111, 116, 119, 124, 127, 132, 135, 140, 143, 148, 151, 156, 159, 164, 167, 172, 175, 180, 183, 188, 191, 196, 199, 204, 207, 212, 215, 220, 223, 228, 231
OFFSET
1,1
COMMENTS
Union of A004771 and A017113.
FORMULA
a(n) = 8*n - a(n-1) - 5 (with a(1)=4). - Vincenzo Librandi, Aug 06 2010
a(n) = 4*n -(1 + (-1)^n)/2. - Arkadiusz Wesolowski, Sep 18 2012
G.f.: x*(4+3*x+x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 10 2015
From Franck Maminirina Ramaharo, Jul 22 2018: (Start)
a(n) = A047470(n) + 4.
E.g.f.: (2 - exp(-x) + (8*x - 1)*exp(x))/2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 - log(2)/4 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021
MAPLE
A047535:=n->4*n - (1 + (-1)^n)/2; seq(A047535(n), n=1..100); # Wesley Ivan Hurt, Feb 24 2014
MATHEMATICA
Table[4n - (1 + (-1)^n)/2, {n, 100}] (* Wesley Ivan Hurt, Feb 24 2014 *)
PROG
(Maxima) makelist(4*n - (1 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 22 2018 */
(Python)
def A047535(n): return (n<<2)-(n&1^1) # Chai Wah Wu, Mar 30 2024
KEYWORD
nonn,easy
STATUS
approved