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%I #18 Mar 16 2022 16:19:28
%S 0,1,3,1,2,4,2,4,3,1,2,4,2,3,5,3,5,4,2,3,5,3,4,6,5,4,3,1,2,4,2,3,5,3,
%T 5,4,2,3,5,3,4,6,4,6,5,3,4,6,4,5,7,6,5,4,2,3,5,3,4,6,4,6,5,3,4,6,4,5,
%U 7,5,7,6,4,5,7,5,6,9,5,4,3,1,2,4,2,3,5,3,5,4,2
%N Write numbers in ternary under each other (right justified), read diagonals in SW-NE direction, sum digits.
%C The digit sum of A102370 "sloping binary numbers" equals A089400. What about "sloping numbers" and their digit sums in other bases?
%e Numbers written in ternary:
%e 0
%e 1
%e 2
%e 10
%e 11
%e 12
%e 20
%e 21
%e 22
%e 100
%e 101
%e 102
%e .....
%e The NW-SE diagonals are:
%e 0
%e 1
%e 12
%e 10
%e 11
%e 22
%e 20
%e 121
%e 102
%e ......
%e giving 0, 1, 3, 1, 2, 4, 2, 4, 3, 1, 2, 4, ...
%o (PARI) lista(nn) = {my(v = vector(nn), nb); for (n=1, nn, v[n] = digits(n-1, 3); nb = #v[n];); for (n=1, nn, if (#v[n] < nb, v[n] = concat(vector(nb-#v[n]), v[n]));); my(list = List()); for (n=nb, nn, my(s=0, pos=1); forstep(k=n, n-nb+1, -1, s += (v[k])[pos]; pos++;); listput(list, s);); Vec(list);} \\ _Michel Marcus_, Mar 16 2022
%Y Cf. A102370.
%K nonn,base
%O 1,3
%A _Ctibor O. Zizka_, Dec 22 2007
%E New name using formula and more terms from _Michel Marcus_, Mar 16 2022
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