A067103
a(n) = floor(X/Y), where X = concatenation of cubes and Y = concatenation of natural numbers.
Original entry on oeis.org
1, 1, 14, 148, 14804, 1480398, 148039049, 14803895356, 1480389427723, 148038942652481, 14803894265116205, 1480389426511476635, 148038942651147507639, 14803894265114750596056, 1480389426511475059425814, 148038942651147505942389607, 14803894265114750594238756940
Offset: 1
a(6) = floor(182764125216/123456) = floor(1480398.888802...) = 1480398.
Cf.
A067091,
A067092,
A067093,
A067094,
A067095,
A067096,
A067097,
A067098,
A067099,
A067100,
A067101,
A067102.
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a:= n-> floor(parse(cat(i^3$i=1..n))/parse(cat($1..n))):
seq(a(n), n=1..17); # Alois P. Heinz, May 25 2022
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f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[k^3]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 20} ]
nn=20;With[{c=Table[IntegerDigits[n^3],{n,nn}],s=Table[IntegerDigits[n],{n,nn}]}, Table[Floor[FromDigits[Flatten[Take[c,i]]]/FromDigits[Flatten[Take[s,i]]]],{i,nn}]] (* Harvey P. Dale, Feb 10 2013 *)
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c1(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); \\ A007908
c3(n) = my(s=""); for(k=1, n, s=Str(s, k^3)); eval(s); \\ A019522
a(n) = c3(n)\c1(n); \\ Michel Marcus, May 25 2022
A067104
a(n) = floor[ X/Y], where X = concatenation of first n factorials and Y = concatenation of first n natural numbers.
Original entry on oeis.org
1, 1, 1, 10, 1022, 102256, 102255452, 1022553862210, 102255378766606673, 10225537868377981588347, 10225537868286872045185666318, 102255378682858781228966381713174081, 10225537868285867355405173700779791589867289
Offset: 1
a(5) = floor [12624120/12345] = floor[1022.60996354799513973268529769137] = 1022.
Cf.
A067091,
A067092,
A067093,
A067094,
A067095,
A067096,
A067097,
A067098,
A067099,
A067100,
A067101,
A067102,
A067103.
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Table[Floor[FromDigits[Flatten[IntegerDigits/@(Range[n]!)]]/FromDigits[ Flatten[IntegerDigits/@Range[n]]]],{n,15}] (* Harvey P. Dale, Jun 09 2020 *)
Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003
A067105
a(n) = floor[ X/Y], where X = concatenation of k^k from 1 up to n^n and Y = concatenation of 1, ..., n.
Original entry on oeis.org
1, 1, 11, 1156, 1156141, 11560850121, 1156078457100065, 11560777079611640798854, 1156077623683098402586161358986, 1156077622746675519639905953267558458549
Offset: 1
a(5) = floor [14272563125/12345] = floor[1156141.20089104900769542324827866] = 1156141.
Cf.
A067091,
A067092,
A067093,
A067094,
A067095,
A067096,
A067097,
A067098,
A067099,
A067100,
A067101,
A067102,
A067103,
A067104.
-
fxy[n_]:=Module[{num=FromDigits[Flatten[IntegerDigits/@(Table[x^x,{x,n}])]], den=FromDigits[Flatten[IntegerDigits/@Range[n]]]},Floor[num/den]]; Array[ fxy,10] (* Harvey P. Dale, Mar 21 2013 *)
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003
Showing 1-3 of 3 results.
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