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A057541 Birthday set of order 9: i.e., numbers congruent to +- 1 modulo 2, 3, 4, 5, 6, 7, 8 and 9. 4
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 (list; graph; refs; listen; history; text; internal format)
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 +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

EXAMPLE

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.

PROG

(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

CROSSREFS

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

Sequence in context: A142304 A201313 A078949 * A268889 A142432 A250982

Adjacent sequences:  A057538 A057539 A057540 * A057542 A057543 A057544

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

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Last modified January 24 07:18 EST 2020. Contains 331189 sequences. (Running on oeis4.)