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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 02:42 EDT 2020. Contains 334647 sequences. (Running on oeis4.)