A066599 a(n) = smallest number which can be expressed as the product of a number and its reversal in exactly n different ways.

1, 2520, 635040, 1015560, 10119126106147652568, 11158922880, 5918858243794044864, 1046458990080

Offset

1,2

Comments

a(6) = 11158922880 and a(8) = 1046458990080.

a(10) = 101191261061476525680, a(12) = 62624600899319949840, a(14) = 59188582437940448640. - Chai Wah Wu, Apr 16 2019

Links

Table of n, a(n) for n=1..8.

Shyam Sunder Gupta, Equal Product of Reversible Numbers (EPRN), Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 12, 353-365.

Example

a(1) = 1 = 1*1; a(2) = 2520 = 120*21 = 210*12; a(3) = 635040 = 1440*441 = 2520*252 = 4410*144; a(4) = 1015560 = 1560*651 = 2730*372 = 3720*273 = 6510*156; a(6) = 11158922880 = 132480*84231 = 231840*48132 = 275040*40572 = 405720*27504 = 481320*23184 = 842310*13248; a(8) = 1236480*846321 = 2163840*483612 = 2329440*449232 = 2567040*407652 = 4076520*256704 = 4492320*232944 = 4836120*216384 = 8463210*123648.
From Chai Wah Wu, Apr 16 2019: (Start)
a(5) = 10119126106147652568 = 8848263411 * 1143628488 = 8044687521 * 1257864408 = 4884561702 * 2071654884 = 4440958722 * 2278590444 = 4082378742 * 2478732804
a(7) = 5918858243794044864 = 4834624221 * 1224264384 = 4439423331 * 1333249344 = 4036246641 * 1466426304 = 2762642412 * 2142462672 = 2566246032 * 2306426652 = 2536813332 * 2333186352 = 2511746532 * 2356471152
a(10) = 101191261061476525680 = 88482634110 * 1143628488 = 80446875210 * 1257864408 = 48845617020 * 2071654884 = 44409587220 * 2278590444 = 40823787420 * 2478732804 = 24787328040 * 4082378742 = 22785904440 * 4440958722 = 20716548840 * 4884561702 = 12578644080 * 8044687521 = 11436284880 * 8848263411
a(12) = 62624600899319949840 = 46891553310 * 1335519864 = 46055795310 * 1359755064 = 42632986410 * 1468923624 = 28946436120 * 2163464982 = 26795173320 * 2337159762 = 26317597320 * 2379571362 = 23795713620 * 2631759732 = 23371597620 * 2679517332 = 21634649820 * 2894643612 = 14689236240 * 4263298641 = 13597550640 * 4605579531 = 13355198640 * 4689155331
a(14) = 59188582437940448640 = 48346242210 * 1224264384 = 44394233310 * 1333249344 = 40362466410 * 1466426304 = 27626424120 * 2142462672 = 25662460320 * 2306426652 = 25368133320 * 2333186352 = 25117465320 * 2356471152 = 23564711520 * 2511746532 = 23331863520 * 2536813332 = 23064266520 * 2566246032 = 21424626720 * 2762642412 = 14664263040 * 4036246641 = 13332493440 * 4439423331 = 12242643840 * 4834624221
(End)

Mathematica

f[n_] := (m = ToExpression[StringReverse[ToString[n]]]; If[n >= m, n*m, 0]); a = Sort[Table[f[n], {n, 0, 10^7}]]; While[a[[1]] == 0, a = Drop[a, 1]]; Do[k = 1; While[ a[[k]] != a[[k + n - 1]], k++ ]; Print[ a[[k]]], {n, 1, 4} ]

Crossrefs

Cf. A066531.

Sequence in context: A064592 A179722 A109480 * A107531 A123485 A282433

Adjacent sequences: A066596 A066597 A066598 * A066600 A066601 A066602

Keyword

nonn

Author

Robert G. Wilson v, Jan 08 2002

Extensions

a(5) and a(7) from Chai Wah Wu, Apr 16 2019

Definition corrected by N. J. A. Sloane, Aug 01 2019

Status

approved