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A066599
a(n) = smallest number which can be expressed as the product of a number and its reversal in exactly n different ways.
0
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
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
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