A057541 - OEIS

%I #21 Feb 20 2022 12:06:33

%S 1,71,449,559,631,881,1009,1079,1441,1511,1639,1889,1961,2071,2449,

%T 2519,2521,2591,2969,3079,3151,3401,3529,3599,3961,4031,4159,4409,

%U 4481,4591,4969,5039,5041,5111,5489,5599,5671,5921,6049,6119,6481,6551,6679

%N Birthday set of order 9: i.e., numbers congruent to +- 1 modulo 2, 3, 4, 5, 6, 7, 8 and 9.

%H Ray Chandler, <a href="/A057541/b057541.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Colin Barker)

%H A. Feist, <a href="http://www.kappamuepsilon.org/pages/a/Pentagon/Vol_60_Num_1_Fall_2000.pdf">On the Density of Birthday Sets</a>, The Pentagon, 60 (No. 1, Fall 2000), 31-35.

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

%F G.f.: x*(x^16 +70*x^15 +378*x^14 +110*x^13 +72*x^12 +250*x^11 +128*x^10 +70*x^9 +362*x^8 +70*x^7 +128*x^6 +250*x^5 +72*x^4 +110*x^3 +378*x^2 +70*x +1) / ((x -1)^2*(x +1)*(x^2 +1)*(x^4 +1)*(x^8 +1)). - _Colin Barker_, Mar 16 2015

%e 5599 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, -1 mod 8 and 1 mod 9.

%t LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1},{1,71,449,559,631,881,1009,1079,1441,1511,1639,1889,1961,2071,2449,2519,2521},80] (* _Harvey P. Dale_, Feb 20 2022 *)

%o (PARI) Vec(x*(x^16 +70*x^15 +378*x^14 +110*x^13 +72*x^12 +250*x^11 +128*x^10 +70*x^9 +362*x^8 +70*x^7 +128*x^6 +250*x^5 +72*x^4 +110*x^3 +378*x^2 +70*x +1) / ((x -1)^2*(x +1)*(x^2 +1)*(x^4 +1)*(x^8 +1)) + O(x^100)) \\ _Colin Barker_, Mar 16 2015

%Y Cf. A007310, A057538, A057539 and A057540 are other birthday sets.

%K nonn,easy

%O 1,2

%A Andrew R. Feist (andrewf(AT)math.duke.edu), Sep 06 2000

%E Offset corrected to 1 by _Ray Chandler_, Jul 29 2019