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%I #14 Dec 09 2018 12:30:57
%S 1,4,7,28,31,34,55,58,61,244,247,250,271,274,277,298,301,304,487,490,
%T 493,514,517,520,541,544,547,2188,2191,2194,2215,2218,2221,2242,2245,
%U 2248,2431,2434,2437,2458,2461,2464,2485,2488,2491,2674,2677,2680,2701,2704,2707,2728,2731,2734
%N Positive integers a(n) such that for every integer m == 1 (mod 3), m >= 4, there exists a unique representation of m as a sum of the form a(l) + 3*a(s).
%C Theorem. An integer is in the sequence iff in its expansion on base 3 all digits at the k-th position from the end, k=3, 5, 7, ..., are zeros while the first digit from the end is 1. To get the decomposition of m==1(mod 3) as sum a(l)+3a(s), write m-3 as Sum b_j 3^j, then a(l) = 1 + Sum_{j odd} b_j 3^j.
%e If m=46, then we have 46=1*3^0+2*3^2+1*3^3, thus a(l)=1+1*3^3=28 and the required decomposition is: 46=28+3*4, such that a(s)=4. We see that l=4, s=2, i.e. "index coordinates" of 46 are (4, 2). Thus we have a one-to-one map of integers m==1(mod 3), m>=4, to the positive lattice points on the plane.
%o (PARI) isok(n) = {my(d=Vecrev(digits(n, 3)), k=3); while (k <= #d, if (d[k], return (0)); k += 2;); d[1] == 1;} \\ _Michel Marcus_, Dec 09 2018
%Y Cf. A145812, A145818.
%K nonn
%O 1,2
%A _Vladimir Shevelev_, Oct 27 2008
%E More terms from _Michel Marcus_, Dec 09 2018
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