cp's OEIS Frontend

A003662 a(n) is smallest number != a(j) + a(k), j < k and a(1) = 1, a(2) = 4.

%I A003662 M3273 #38 Mar 13 2023 06:53:15
%S A003662 1,4,6,8,11,13,16,18,23,25,28,30,35,37,40,42,47,49,52,54,59,61,64,66,
%T A003662 71,73,76,78,83,85,88,90,95,97,100,102,107,109,112,114,119,121,124,
%U A003662 126,131,133,136,138,143,145,148,150,155,157,160,162,167,169,172,174,179,181,184
%N A003662 a(n) is smallest number != a(j) + a(k), j < k and a(1) = 1, a(2) = 4.
%D A003662 R. K. Guy, "s-Additive sequences", preprint, 1994.
%D A003662 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003662 Colin Barker, <a href="/A003662/b003662.txt">Table of n, a(n) for n = 1..1000</a>
%H A003662 R. K. Guy, <a href="/A007300/a007300.pdf">s-Additive sequences</a>, Preprint, 1994. (Annotated scanned copy)
%H A003662 Aayush Rajasekaran, <a href="https://uwspace.uwaterloo.ca/bitstream/handle/10012/13202/Rajasekaran_Aaayush.pdf?sequence=3">Using Automata Theory to Solve Problems in Additive Number Theory</a>, MS thesis, University of Waterloo, 2018.
%H A003662 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A003662 Numbers congruent to {1, 4, 6, 11} mod 12 plus the number 8.
%F A003662 a(n) = a(n-1) + a(n-4) - a(n-5) for n > 7. - _Colin Barker_, Feb 27 2015
%F A003662 G.f.: x*(2*x^8 + x^6 - x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 3*x + 1) / ((x-1)^2*(x+1)*(x^2+1)). - _Colin Barker_, Feb 27 2015
%t A003662 Sort[Join[{8},Select[Range[200],MemberQ[{1,4,6,11},Mod[#,12]]&]]] (* _Harvey P. Dale_, Apr 26 2011 *)
%o A003662 (PARI) Vec(x*(2*x^8+x^6-x^5+2*x^4+2*x^3+2*x^2+3*x+1)/((x-1)^2*(x+1)*(x^2+1)) + O(x^100)) \\ _Colin Barker_, Feb 27 2015
%Y A003662 Cf. A060469.
%Y A003662 Cf. A003666.
%K A003662 nonn,easy
%O A003662 1,2
%A A003662 _N. J. A. Sloane_, _Mira Bernstein_
%E A003662 Name clarified by _David A. Corneth_, Mar 13 2023