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 A140103 Term-by-term sums of A140101 and A140100; also, equals the complement of A140102, which is the term-by-term differences of A140101 and A140100, where A140101 is the complement of A140100. 15
 3, 8, 12, 17, 20, 25, 29, 34, 39, 43, 48, 51, 56, 60, 65, 69, 74, 77, 82, 86, 91, 96, 100, 105, 108, 113, 117, 122, 125, 130, 134, 139, 144, 148, 153, 156, 161, 165, 170, 174, 179, 182, 187, 191, 196, 201, 205, 210, 213, 218, 222, 227, 232, 236, 241, 244, 249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: a(n) = A003145(n) + n. This is the most direct connection between the Greedy Queens sequence and the tribonacci word that I know. - Michel Dekking, Mar 19 2019. [My notes show that I made this conjecture on Jul 20 2018. There are many similar conjectures relating the two problems. For example A140100 = A003145(n)-A003144(n), A140101(n) = A003146(n)-A003145(n), a(n) = A003146(n)-A003144(n). - N. J. A. Sloane, Mar 19 2019] All these conjectures are now theorems - see the Dekking et al. paper. - N. J. A. Sloane, Jul 22 2019 REFERENCES Robbert Fokkink, Gerard Francis Ortega, Dan Rust, Corner the Empress, arXiv:2204.11805. See Table 2. LINKS N. J. A. Sloane, Table of n, a(n) for n=1..50000, Sep 13 2016 (First 1001 terms from Reinhard Zumkeller) F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52. N. J. A. Sloane, Maple program for A140100, A140101, A140102, A140103 FORMULA a(n) = A140100(n) + A140101(n). Conjecture: the limit of A140103(n)/A140102(n) = t^2 = 3.38297576... (cf. A276800) where the limit of A140101(n)/A140100(n) = t = 1.839286755.. and t = tribonacci constant satisfies: t^3 = 1 + t + t^2. MAPLE See link. MATHEMATICA nmax = 100; y[0] = 0; x[1] = 1; y[1] = 2; x[n_] := x[n] = For[yn = y[n-1] + 1, True, yn++, For[xn = x[n-1] + 1, xn < yn, xn++, xx = Array[x, n-1]; yy = Array[y, n-1]; If[FreeQ[xx, xn | yn] && FreeQ[yy, xn | yn] && FreeQ[yy - xx, yn - xn] && FreeQ[yy + xx, yn - xn], y[n] = yn; Return[xn]]]]; Do[x[n], {n, 1, nmax}]; yy + xx (* Jean-François Alcover, Aug 01 2018 *) PROG (PARI) {X=[1]; Y=[2]; D=[1]; S=[3]; print1(Y[1]-X[1]", "); for(n=1, 100, for(j=2, 2*n, if(setsearch(Set(concat(X, Y)), j)==0, Xt=concat(X, j); for(k=j+1, 3*n, if(setsearch(Set(concat(Xt, Y)), k)==0, if(setsearch(Set(concat(D, S)), k-j)==0, if(setsearch(Set(concat(D, S)), k+j)==0, X=Xt; Y=concat(Y, k); D=concat(D, k-j); S=concat(S, k+j); print1(Y[ #X]-X[ #Y]", "); break); break))))))} CROSSREFS Cf. A140102 (complement); A140100, A140101; A058265, A276800. For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394. Sequence in context: A183991 A022806 A084162 * A190374 A189758 A190368 Adjacent sequences: A140100 A140101 A140102 * A140104 A140105 A140106 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 04 2008 EXTENSIONS Terms computed by Reinhard Zumkeller STATUS approved

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