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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

%I #11 Aug 01 2019 01:17:06

%S 1,2520,635040,1015560,10119126106147652568,11158922880,

%T 5918858243794044864,1046458990080

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

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

%C a(10) = 101191261061476525680, a(12) = 62624600899319949840, a(14) = 59188582437940448640. - _Chai Wah Wu_, Apr 16 2019

%e 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.

%e From _Chai Wah Wu_, Apr 16 2019: (Start)

%e a(5) = 10119126106147652568 = 8848263411 * 1143628488 = 8044687521 * 1257864408 = 4884561702 * 2071654884 = 4440958722 * 2278590444 = 4082378742 * 2478732804

%e a(7) = 5918858243794044864 = 4834624221 * 1224264384 = 4439423331 * 1333249344 = 4036246641 * 1466426304 = 2762642412 * 2142462672 = 2566246032 * 2306426652 = 2536813332 * 2333186352 = 2511746532 * 2356471152

%e a(10) = 101191261061476525680 = 88482634110 * 1143628488 = 80446875210 * 1257864408 = 48845617020 * 2071654884 = 44409587220 * 2278590444 = 40823787420 * 2478732804 = 24787328040 * 4082378742 = 22785904440 * 4440958722 = 20716548840 * 4884561702 = 12578644080 * 8044687521 = 11436284880 * 8848263411

%e 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

%e 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

%e (End)

%t 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} ]

%Y Cf. A066531.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 08 2002

%E a(5) and a(7) from _Chai Wah Wu_, Apr 16 2019

%E Definition corrected by _N. J. A. Sloane_, Aug 01 2019

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)