A305130 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.

10, 11, 12, 18, 22, 33, 44, 55, 66, 77, 88, 99, 101, 110, 121, 132, 141, 165, 181, 201, 202, 221, 222, 261, 262, 282, 302, 303, 322, 323, 342, 343, 363, 403, 404, 423, 424, 444, 463, 483, 504, 505, 525, 545, 564, 584, 585, 605, 606, 645, 646, 666, 686, 706

Offset

1,1

Comments

These numbers are related to the taxicab number 1729. This is why they might be called "additive Hardy-Ramanujan numbers".

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Viorel Nitica, About some relatives of the taxicab numbers, submitted to Journal of Integer Sequences, (2018). [Where these numbers are introduced.]

Viorel Niţică, Jeroz Makhania, About the Orbit Structure of Sequences of Maps of Integers, Symmetry (2019), Vol. 11, No. 11, 1374.

Example

For k = 11 the sum of the digits is 2 and the multiplier is 5: 2 * 5 = 10 and 10 + 01 = 11.
For k = 747 the sum of the digits is 18 and the multiplier is 7: 18 * 7 = 126 and 126 + 621 = 747.

Mathematica

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 *)

Crossrefs

Subsequence of A067030.

Cf. A004086, A011541, A305131.

Sequence in context: A219251 A154770 A320601 * A098395 A207968 A207671

Adjacent sequences: A305127 A305128 A305129 * A305131 A305132 A305133

Keyword

nonn,base

Author

Viorel Nitica, May 26 2018

Status

approved