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A342261 Irregular triangular array T(n,k) = m read by rows. Row n lists all solutions m < 3^n, where A340407(3^n*j - m) = n is true for all j > 0, sorted in ascending order.

%I A342261 #28 Jul 13 2022 21:58:41
%S A342261 0,1,8,2,4,5,16,13,14,22,34,38,52,74,77,20,25,40,50,88,130,146,173,
%T A342261 185,203,209,223,229,230,238,241,130,146,173,185,203,209,223,229,230,
%U A342261 238,241,41,61,76,104,106,121,128,157,254,266,292,311,403,412,430,445,454,493
%N A342261 Irregular triangular array T(n,k) = m read by rows. Row n lists all solutions m < 3^n, where A340407(3^n*j - m) = n is true for all j > 0, sorted in ascending order.
%C A342261 Each row n has 2^(n-1) values.
%C A342261 In all rows other than the first row of T(n,k), there are exactly 2^(n-2) numbers of the form 3*p + 1 and the same number of numbers of the form 3*q - 1.
%C A342261 Each integer has a unique representation of the form 3^n*j - T(n,k).
%e A342261 Triangle T(n,k) begins:
%e A342261   0;
%e A342261   1,   8;
%e A342261   2,   4,  5, 16;
%e A342261   13, 14, 22, 34, 38, 52, 74, 77;
%o A342261 (MATLAB)
%o A342261 function t = A342261 (max_row)
%o A342261     maxtest = 10;
%o A342261     d = A340407(maxtest*3^max_row);
%o A342261     for row = 1:max_row
%o A342261         m = 0;
%o A342261         for k = 1:2^(row-1)
%o A342261             test = d((1:maxtest)*(3^row)-m);
%o A342261             while ~all(test == test(1))||(test(1) ~= row)
%o A342261                 m = m+1;
%o A342261                 test = d((1:maxtest)*(3^row)-m);
%o A342261             end
%o A342261             t(row,k) = m;
%o A342261             t = t+1;
%o A342261         end
%o A342261     end
%o A342261 end
%o A342261 function d = A340407 (max_p)
%o A342261     for p = 1:max_p
%o A342261         s = 6*p -2;
%o A342261         c = 0;
%o A342261         while mod(s,3) ~= 0
%o A342261             s = A342369( s );
%o A342261            if mod(s,3) == 2
%o A342261                 c = c+1;
%o A342261             end
%o A342261         end
%o A342261         d(p) = c;
%o A342261     end
%o A342261 end
%o A342261 function b = A342369( n )
%o A342261     if mod(n,3) == 2
%o A342261         b = (2*n - 1)/3;
%o A342261     else
%o A342261         b = 2*n;
%o A342261     end
%o A342261 end
%Y A342261 Cf. A340407.
%K A342261 nonn,tabf
%O A342261 1,3
%A A342261 _Thomas Scheuerle_, Mar 26 2021