cp's OEIS Frontend

A304868 Numbers x satisfying x == 1 (mod 4) or x == 14, 26, 30 (mod 32).

%I A304868 #15 May 20 2018 13:48:48
%S A304868 1,5,9,13,14,17,21,25,26,29,30,33,37,41,45,46,49,53,57,58,61,62,65,69,
%T A304868 73,77,78,81,85,89,90,93,94,97,101,105,109,110,113,117,121,122,125,
%U A304868 126,129,133,137,141,142,145,149,153,154,157,158,161,165,169,173,174,177
%N A304868 Numbers x satisfying x == 1 (mod 4) or x == 14, 26, 30 (mod 32).
%C A304868 The sum of two distinct terms of this sequence is never a square.
%C A304868 Sequence has density 11/32, the maximal density that can be attained with such a sequence.
%D A304868 J. P. Massias, Sur les suites dont les sommes des termes 2 à 2 ne sont pas des carrés, Publications du département de mathématiques de Limoges, 1982.
%H A304868 Colin Barker, <a href="/A304868/b304868.txt">Table of n, a(n) for n = 1..1000</a>
%H A304868 J. C. Lagarias, A. M. Odlyzko, J. B. Shearer, <a href="http://dx.doi.org/10.1016/0097-3165(82)90005-X">On the density of sequences of integers the sum of no two of which is a square. I. Arithmetic progressions</a>, Journal of Combinatorial Theory. Series A, 33 (1982), pp. 167-185.
%H A304868 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,1,-1).
%F A304868 From _Colin Barker_, May 20 2018: (Start)
%F A304868 G.f.: x*(1 + 4*x + 4*x^2 + 4*x^3 + x^4 + 3*x^5 + 4*x^6 + 4*x^7 + x^8 + 3*x^9 + x^10 + 2*x^11) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)).
%F A304868 a(n) = a(n-1) + a(n-11) - a(n-12) for n>12.
%F A304868 (End)
%o A304868 (PARI) isok(n) = ((n%4)==1) || ((n%32)==14) || ((n%32)==26) || ((n%32)==30);
%o A304868 (PARI) Vec(x*(1 + 4*x + 4*x^2 + 4*x^3 + x^4 + 3*x^5 + 4*x^6 + 4*x^7 + x^8 + 3*x^9 + x^10 + 2*x^11) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)) + O(x^40)) \\ _Colin Barker_, May 20 2018
%Y A304868 Cf. A016777 (another such sequence), A210380.
%K A304868 nonn,easy
%O A304868 1,2
%A A304868 _Michel Marcus_, May 20 2018