OFFSET
1,2
COMMENTS
Also the numbers k such that 10^p+k could possibly be prime. - Roderick MacPhee, Nov 20 2011 This statement can be written as follows. If 10^m + k = prime, for any m >= 1, then k is in this sequence. See the pink box comments by Roderick MacPhee from Dec 09 2014. - Wolfdieter Lang, Dec 09 2014
The odd-indexed terms are one more than the arithmetic mean of their neighbors; the even-indexed terms are one less than the arithmetic mean of their neighbors. - Amarnath Murthy, Jul 29 2003
Partial sums are A212959. - Philippe Deléham, Mar 16 2014
12*a(n) is conjectured to be the length of the boundary after n iterations of the hexagon and square expansion shown in the link. The squares and hexagons have side length 1 in some units. The pattern is supposed to become the planar Archimedean net 4.6.12 when n -> infinity. - Kival Ngaokrajang, Nov 30 2014
Positive numbers k for which 1/2 + k/3 + k^2/6 is an integer. - Bruno Berselli, Apr 12 2018
REFERENCES
L. Lovasz, J. Pelikan, K. Vesztergombi, Discrete Mathematics, Springer (2003); 14.4, p. 225.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
L. Lovász, J. Pelikán and K. Vesztergombi, Discrete Mathematics, Elementary and Beyond, Springer (2003); 14.4, p. 225.
Kival Ngaokrajang, Illustration of initial terms.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
From Paul Barry, Sep 04 2003: (Start)
O.g.f.: (1 + 2*x + 3*x^2)/((1 + x)*(1 - x)^2) = (1 + 2*x + 3*x^2)/((1 - x)*(1 - x^2)).
E.g.f.: (6*x + 1)*exp(x)/2 + exp(-x)/2;
a(n) = 3*n - 5/2 - (-1)^n/2. (End)
a(n) = 2*floor((n-1)/2) + 2*n - 1. - Gary Detlefs, Mar 18 2010
a(n) = 6*n - a(n-1) - 8 with n > 1, a(1)=1. - Vincenzo Librandi, Aug 05 2010
a(n) = 3*n - 2 - ((n+1) mod 2). - Wesley Ivan Hurt, Jun 29 2013
a(1)=1, a(2)=3, a(3)=7; for n>3, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Oct 01 2013
From Benedict W. J. Irwin, Apr 13 2016: (Start)
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(4*sqrt(3)) + log(3)/4. - Amiram Eldar, Dec 11 2021
MAPLE
seq(3*k-2-((k+1) mod 2), k=1..100); # Wesley Ivan Hurt, Sep 28 2013
MATHEMATICA
Table[{2, 4}, {30}] // Flatten // Prepend[#, 1]& // Accumulate (* Jean-François Alcover, Jun 10 2013 *)
Select[Range[200], MemberQ[{1, 3}, Mod[#, 6]]&] (* or *) LinearRecurrence[{1, 1, -1}, {1, 3, 7}, 70] (* Harvey P. Dale, Oct 01 2013 *)
PROG
(Haskell)
a047241 n = a047241_list !! (n-1)
a047241_list = 1 : 3 : map (+ 6) a047241_list
-- Reinhard Zumkeller, Feb 19 2013
(PARI) a(n)=bitor(3*n-3, 1) \\ Charles R Greathouse IV, Sep 28 2013
(Python) for n in range(1, 10**5):print(3*n-2-((n+1)%2)) # Soumil Mandal, Apr 14 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Formula corrected by Bruno Berselli, Jun 24 2010
STATUS
approved