A057539 - OEIS

%I #36 Jul 31 2021 21:58:48

%S 1,29,41,71,139,169,181,209,211,239,251,281,349,379,391,419,421,449,

%T 461,491,559,589,601,629,631,659,671,701,769,799,811,839,841,869,881,

%U 911,979,1009,1021,1049,1051,1079,1091,1121,1189,1219,1231,1259,1261,1289

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

%C Integers of the form sqrt(840*k+1) for k >= 0. - _Boyd Blundell_, Jul 10 2021

%H Ray Chandler, <a href="/A057539/b057539.txt">Table of n, a(n) for n = 1..10000</a>

%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_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).

%F 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

%F a(n) = a(n-8) + 210 = a(n-1) + a(n-8) - a(n-9). - _Charles R Greathouse IV_, Oct 20 2014

%F a(n) = 105n/4 + O(1). - _Charles R Greathouse IV_, Oct 20 2014

%t 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 *)

%o (PARI) is_A057539(n,m=[2,3,4,5,6,7])=!for(i=1,#m,abs((n+1)%m[i]-1)==1||return)

%o (PARI) is(n)=for(i=4,7,if(abs(centerlift(Mod(n,i)))!=1, return(0))); 1 \\ _Charles R Greathouse IV_, Oct 20 2014

%o (Python)

%o def ok(n): return all(n%d in [1, d-1] for d in range(2, 8))

%o def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]

%o print(aupto(1300)) # _Michael S. Branicky_, Jan 29 2021

%Y Cf. A057538, A057540, A057541.

%K easy,nonn

%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