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Number of distinct integers resulting from adding an n-digit non-multiple of 10 and its reverse.
1

%I #35 Mar 31 2024 14:03:13

%S 9,17,170,323,3230,6137,61370,116603,1166030,2215457

%N Number of distinct integers resulting from adding an n-digit non-multiple of 10 and its reverse.

%F For n > 1, empirically a(n+1) = 10 a(n) if n even, 19 a(n) / 10 if n odd, and thus a(n+2) = 19 a(n). - _Michael S. Branicky_, Mar 31 2024

%e For n=2 there are 81 2-digit numbers not ending with 0: {11, 12, 13, ..., 99}. There are 17 distinct results when adding each of these to their reversal: {22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198}. Therefore a(2) = 17.

%t A371031[n_] :=

%t Module[{nn, ss},

%t nn = Select[Range[If[n == 1, 1, 10^(n - 1) + 1], 10^n - 1], Mod[#, 10] > 0 &];

%t ss = Map[# + FromDigits[Reverse[IntegerDigits[#]]] &, nn];

%t Return[CountDistinct[ss]]

%t ];

%t Map[A371031[#]&, Range[7]]

%Y Cf. A056964, A067251, A358985.

%K nonn,base,more

%O 1,1

%A _César Eliud Lozada_, Mar 08 2024

%E a(9)-a(10) from _Michael S. Branicky_, Mar 30 2024