A057541 Birthday set of order 9: i.e., numbers congruent to +- 1 modulo 2, 3, 4, 5, 6, 7, 8 and 9.

1, 71, 449, 559, 631, 881, 1009, 1079, 1441, 1511, 1639, 1889, 1961, 2071, 2449, 2519, 2521, 2591, 2969, 3079, 3151, 3401, 3529, 3599, 3961, 4031, 4159, 4409, 4481, 4591, 4969, 5039, 5041, 5111, 5489, 5599, 5671, 5921, 6049, 6119, 6481, 6551, 6679

Offset: 1

Author

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

Keywords

• nonn
• easy

Examples

			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.
		

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).

Crossrefs

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

Programs

Mathematica

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 *)

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

Formula

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

Extensions

Offset corrected to 1 by Ray Chandler, Jul 29 2019