A057539 Birthday set of order 7, i.e., numbers congruent to +- 1 modulo 2, 3, 4, 5, 6 and 7.

1, 29, 41, 71, 139, 169, 181, 209, 211, 239, 251, 281, 349, 379, 391, 419, 421, 449, 461, 491, 559, 589, 601, 629, 631, 659, 671, 701, 769, 799, 811, 839, 841, 869, 881, 911, 979, 1009, 1021, 1049, 1051, 1079, 1091, 1121, 1189, 1219, 1231, 1259, 1261, 1289

Offset

1,2

Comments

Integers of the form sqrt(840*k+1) for k >= 0. - Boyd Blundell, Jul 10 2021

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

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 (1,0,0,0,0,0,0,1,-1).

Formula

G.f.: x*(1 + 28*x + 12*x^2 + 30*x^3 + 68*x^4 + 30*x^5 + 12*x^6 + 28*x^7 + x^8) / ((1+x)*(x^2+1)*(x^4+1)*(x-1)^2). - R. J. Mathar, Oct 08 2011

a(n) = a(n-8) + 210 = a(n-1) + a(n-8) - a(n-9). - Charles R Greathouse IV, Oct 20 2014

a(n) = 105n/4 + O(1). - Charles R Greathouse IV, Oct 20 2014

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 29, 41, 71, 139, 169, 181, 209, 211}, 50] (* Harvey P. Dale, Sep 24 2014 *)

Prog

(PARI) is_A057539(n, m=[2, 3, 4, 5, 6, 7])=!for(i=1, #m, abs((n+1)%m[i]-1)==1||return)
(PARI) is(n)=for(i=4, 7, if(abs(centerlift(Mod(n, i)))!=1, return(0))); 1 \\ Charles R Greathouse IV, Oct 20 2014
(Python)
def ok(n): return all(n%d in [1, d-1] for d in range(2, 8))
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(1300)) # Michael S. Branicky, Jan 29 2021

Crossrefs

Cf. A057538, A057540, A057541.

Sequence in context: A346145 A058900 A137226 * A157257 A214405 A104072

Adjacent sequences: A057536 A057537 A057538 * A057540 A057541 A057542

Keyword

easy,nonn

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