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

%I A057539 #36 Jul 31 2021 21:58:48
%S A057539 1,29,41,71,139,169,181,209,211,239,251,281,349,379,391,419,421,449,
%T A057539 461,491,559,589,601,629,631,659,671,701,769,799,811,839,841,869,881,
%U A057539 911,979,1009,1021,1049,1051,1079,1091,1121,1189,1219,1231,1259,1261,1289
%N A057539 Birthday set of order 7, i.e., numbers congruent to +- 1 modulo 2, 3, 4, 5, 6 and 7.
%C A057539 Integers of the form sqrt(840*k+1) for k >= 0. - _Boyd Blundell_, Jul 10 2021
%H A057539 Ray Chandler, <a href="/A057539/b057539.txt">Table of n, a(n) for n = 1..10000</a>
%H A057539 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 A057539 <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 A057539 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 A057539 a(n) = a(n-8) + 210 = a(n-1) + a(n-8) - a(n-9). - _Charles R Greathouse IV_, Oct 20 2014
%F A057539 a(n) = 105n/4 + O(1). - _Charles R Greathouse IV_, Oct 20 2014
%t A057539 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 A057539 (PARI) is_A057539(n,m=[2,3,4,5,6,7])=!for(i=1,#m,abs((n+1)%m[i]-1)==1||return)
%o A057539 (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 A057539 (Python)
%o A057539 def ok(n): return all(n%d in [1, d-1] for d in range(2, 8))
%o A057539 def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
%o A057539 print(aupto(1300)) # _Michael S. Branicky_, Jan 29 2021
%Y A057539 Cf. A057538, A057540, A057541.
%K A057539 easy,nonn
%O A057539 1,2
%A A057539 Andrew R. Feist (andrewf(AT)math.duke.edu), Sep 06 2000
%E A057539 Offset corrected to 1 by _Ray Chandler_, Jul 29 2019