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%I #38 Jan 28 2020 22:30:55
%S 10,11,12,18,22,33,44,55,66,77,88,99,101,110,121,132,141,165,181,201,
%T 202,221,222,261,262,282,302,303,322,323,342,343,363,403,404,423,424,
%U 444,463,483,504,505,525,545,564,584,585,605,606,645,646,666,686,706
%N Numbers k with the property that there exists a positive integer M, called multiplier, such that the sum of the digits of k times the multiplier added to the reversal of this product gives k.
%C These numbers are related to the taxicab number 1729. This is why they might be called "additive Hardy-Ramanujan numbers".
%H Alois P. Heinz, <a href="/A305130/b305130.txt">Table of n, a(n) for n = 1..1000</a>
%H Viorel Nitica, <a href="https://arxiv.org/abs/1805.10739">About some relatives of the taxicab numbers</a>, submitted to Journal of Integer Sequences, (2018). [Where these numbers are introduced.]
%H Viorel Niţică, Jeroz Makhania, <a href="https://doi.org/10.3390/sym11111374">About the Orbit Structure of Sequences of Maps of Integers</a>, Symmetry (2019), Vol. 11, No. 11, 1374.
%e For k = 11 the sum of the digits is 2 and the multiplier is 5: 2 * 5 = 10 and 10 + 01 = 11.
%e For k = 747 the sum of the digits is 18 and the multiplier is 7: 18 * 7 = 126 and 126 + 621 = 747.
%t Block[{k, d, j}, Reap[Do[k = 1; d = Total@ IntegerDigits[i]; While[Nor[k > i, Set[j, # + IntegerReverse@ #] == i &[d k]], k++]; If[j == i, Sow[{i, k}]], {i, 720}]][[-1, 1, All, 1]] ] (* _Michael De Vlieger_, Jan 28 2020 *)
%Y Subsequence of A067030.
%Y Cf. A004086, A011541, A305131.
%K nonn,base
%O 1,1
%A _Viorel Nitica_, May 26 2018