A067098
Floor[X/Y] where X = concatenation in increasing order of first n powers of 3 and Y = that of first n natural numbers.
Original entry on oeis.org
3, 3, 31, 318, 31817, 3181548, 3181530396, 3181528335091, 31815281031585777, 31815281005815399552, 318152810055319253966698, 3181528100552883295133046294, 318152810055287994498392866979206
Offset: 1
a(4)= floor [ 392781/1234] = floor[318.299027552674230145867098865478] = 318.
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f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[3^k]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 15} ]
Table[Floor[FromDigits[Flatten[IntegerDigits/@(3^Range[n])]]/ FromDigits[ Flatten[IntegerDigits/@Range[n]]]],{n,15}] (* Harvey P. Dale, Mar 10 2019 *)
A067101
Floor[ X/Y], where X = concatenation of the primes and Y = concatenation of natural numbers.
Original entry on oeis.org
2, 1, 1, 1, 19, 190, 1909, 19092, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 190926, 1909260, 19092601, 190926018, 1909260182, 19092601827, 190926018273
Offset: 1
a(5) = floor [235711/12345]=floor[19.093641150...] = 19.
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f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[Prime[k]]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 25} ]
nn=40;With[{prs=Prime[Range[nn]],nats=Range[nn]},Table[Floor[FromDigits[ Flatten[IntegerDigits/@Take[prs,n]]]/FromDigits[Flatten[IntegerDigits /@Take[nats,n]]]],{n,nn}]] (* Harvey P. Dale, Mar 24 2012 *)
A067102
Floor[ X/Y] where X = concatenation of the squares and Y = concatenation of natural numbers.
Original entry on oeis.org
1, 1, 1, 12, 120, 1208, 12082, 120821, 1208216, 12082165, 120821655, 1208216555, 12082165556, 120821655562, 1208216555626, 12082165556267, 120821655562672, 1208216555626728, 12082165556267282, 120821655562672822
Offset: 1
a(5) = floor [1491625/12345]=floor[] = floor[120.828270554880518428513568246254]=120.
Cf.
A067091,
A067092,
A067093,
A067094,
A067095,
A067096,
A067097,
A067098,
A067099,
A067100,
A067101.
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f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[k^2]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 20} ]
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.
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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 1-6 of 6 results.
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