OFFSET
1,2
COMMENTS
From the following 4 disjoint subsets of natural numbers A = {1}, B = {2}, OP = {odd primes}, C = {composites}, 16 sets are derivable: A000027 versus empty set, A002808 vs A008578, A065091 vs A065090, A000040 vs A018252, A006005 vs {{2} with A002808}, {1} vs {A000027 excluding 1}, {2} versus this sequence, {1, 2} versus Union[OP, C].
a(n) is the sum of the obvious divisors of n, which are 1 and n.
The natural numbers excluding 2 are the order numbers of magic squares. Order 2 magic squares do not exist. - William Walkington, Mar 12 2016
The numbers occurring at least twice in Pascal's triangle (A007318, A003016). - Rick L. Shepherd, Jun 05 2016
LINKS
Wikipedia, Magic square.
Jun Yan, Results on pattern avoidance in parking functions, arXiv:2404.07958 [math.CO], 2024. See p. 4.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: x*(1+x-x^2)/(1-x)^2. - Paul Barry, Aug 05 2004
a(n) = n+1 for n>1, a(n) = a(n-1)+1 for n>2. - Wesley Ivan Hurt, Mar 13 2016
E.g.f.: (x + 1)*(exp(x) - 1). - Ilya Gutkovskiy, Jun 05 2016
a(n) = n + [n>1], a(n) = 1+n-floor(1/n). - Alan Michael Gómez Calderón, May 12 2023
MAPLE
printlevel := -1; a := [1]; T := x->LambertW(-x); f := series(((1+T(x)))/(1-T(x)), x, 77); for m from 3 to 77 do a := [op(a), op(2*m, f)] od; print(a); # Zerinvary Lajos, Mar 28 2009
MATHEMATICA
Join[{1}, Range[3, 100]] (* Wesley Ivan Hurt, Mar 13 2016 *)
Drop[Range[100], {2}] (* Harvey P. Dale, Aug 11 2024 *)
PROG
(PARI) a(n)=n+(n>1) \\ Charles R Greathouse IV, Sep 01 2015
(PARI) x='x+O('x^99); Vec((1+x-x^2)/(1-x)^2) \\ Altug Alkan, Mar 26 2016
(Magma) &cat[[1], [n : n in [3..100]]]; // Wesley Ivan Hurt, Mar 13 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Nov 16 2001
EXTENSIONS
Incorrect formula removed by Charles R Greathouse IV, Mar 18 2010
STATUS
approved