OFFSET
1,2
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Colin Barker)
A. Feist, On the Density of Birthday Sets, The Pentagon, 60 (No. 1, Fall 2000), 31-35.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
FORMULA
G.f.: x*(x^16 +40*x^15 +30*x^14 +98*x^13 +40*x^12 +30*x^11 +42*x^10 +110*x^9 +58*x^8 +110*x^7 +42*x^6 +30*x^5 +40*x^4 +98*x^3 +30*x^2 +40*x +1) / ((x -1)^2*(x +1)*(x^2 +1)*(x^4 +1)*(x^8 +1)). - Colin Barker, Mar 16 2015
EXAMPLE
2129 is on the list because it is congruent to 1 mod 2, -1 mod 3, 1 mod 4, -1 mod 5, -1 mod 6, 1 mod 7 and 1 mod 8.
MATHEMATICA
bso8Q[n_]:=Module[{s1=Mod[n, Range[2, 8]], s2}, s2=Abs[s1-Range[2, 8]]; AllTrue[ Thread[{s1, s2}], MemberQ[#, 1]&]]; Select[Range[2500], bso8Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 18 2021 *)
PROG
(PARI) Vec(x*(x^16 +40*x^15 +30*x^14 +98*x^13 +40*x^12 +30*x^11 +42*x^10 +110*x^9 +58*x^8 +110*x^7 +42*x^6 +30*x^5 +40*x^4 +98*x^3 +30*x^2 +40*x +1) / ((x -1)^2*(x +1)*(x^2 +1)*(x^4 +1)*(x^8 +1)) + O(x^100)) \\ Colin Barker, Mar 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Andrew R. Feist (andrewf(AT)math.duke.edu), Sep 06 2000
EXTENSIONS
Offset corrected to 1 by Ray Chandler, Jul 29 2019
STATUS
approved