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A047406
Numbers that are congruent to {4, 6} mod 8.
8
4, 6, 12, 14, 20, 22, 28, 30, 36, 38, 44, 46, 52, 54, 60, 62, 68, 70, 76, 78, 84, 86, 92, 94, 100, 102, 108, 110, 116, 118, 124, 126, 132, 134, 140, 142, 148, 150, 156, 158, 164, 166, 172, 174, 180, 182, 188, 190, 196, 198, 204, 206, 212, 214, 220, 222, 228
OFFSET
1,1
COMMENTS
In groups of four, add the odd and even numbers (4=1+3, 6=2+4; 12=5+7, 14=6+8; etc.). - George E. Antoniou, Dec 12 2001
The first 250 terms (4 through 998) are the 250 non-occurring Fibonacci number residues modulo 1000; i.e., if leading zeros are supplied as necessary for the terms having fewer than three digits, these are the 250 sets of three digits that never appear as the last three digits of a Fibonacci number. - Jon E. Schoenfield, Jul 05 2010
FORMULA
a(n) = A042964(n)*2.
a(n) = (4*n - 1 - (-1)^n). - Jon E. Schoenfield, Jul 05 2010
a(n) = 8*n - a(n-1) - 6 (with a(1)=4). - Vincenzo Librandi, Aug 05 2010
G.f.: 2*x*(2+x+x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 18 2013: (Start)
a(n) = (8 * ceiling(n/2) - 4) * (n mod 2) + (8 * ceiling(n/2) - 2) * (n+1 mod 2).
a(n) = 8 * ceiling(n/2) - 3 + (-1)^n. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/16 - log(2)/8. - Amiram Eldar, Dec 19 2021
E.g.f.: 2*(1 + 2*x*exp(x) - cosh(x)). - David Lovler, Sep 02 2022
EXAMPLE
a(2) = 8*2 - 4 - 6 = 6;
a(3) = 8*3 - 6 - 6 = 12;
a(4) = 8*4 - 12 - 6 = 14.
MATHEMATICA
Select[Range[230], MemberQ[{4, 6}, Mod[#, 8]] &] (* Amiram Eldar, Dec 19 2021 *)
PROG
(PARI) a(n)=4*n-1-(-1)^n \\ Charles R Greathouse IV, May 20 2013
CROSSREFS
Union of A017113 and A017137.
Cf. A042964.
Sequence in context: A140599 A282280 A320495 * A136415 A310596 A247456
KEYWORD
nonn,easy
STATUS
approved