A072723
Integers which are exactly the concatenation of the first m odd numbers (A019519) divided by their sum (A000290 = m^2).
Original entry on oeis.org
1, 15, 16764334957, 3079163563531047898532266016633501
Offset: 1
a(1) = 1/1 = 1; a(2) = 135/(1+3+5) = 15; a(3) = 1357911131517/(1+3+5+7+9+11+13+15+17) = 16764334957; a(4) = 1357911131517192123252729313335373941/(1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37+39+41) = 3079163563531047898532266016633501.
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Select[Table[FromDigits[Flatten[IntegerDigits/@Range[1,2n+1,2]]]/Total[Range[1,2n+1,2]],{n,0,30}],IntegerQ] (* Harvey P. Dale, Mar 24 2023 *)
A067123
Floor[X/Y] where X = concatenation of first n cubes in increasing order and Y = concatenation of first n squares.
Original entry on oeis.org
1, 1, 12, 12, 122, 1225, 12252, 122526, 1225268, 12252682, 122526828, 1225268284, 12252682845, 122526828457, 1225268284577, 12252682845779, 122526828457797, 1225268284577978, 12252682845779785, 122526828457797852
Offset: 1
a(5) = floor[182764125/1491625] = floor[122.526858292131065113550657839604] = 122.
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fxy[n_]:=Module[{c=FromDigits[Flatten[IntegerDigits/@(Range[n]^3)]],s = FromDigits[ Flatten[ IntegerDigits/@(Range[n]^2)]]}, Floor[c/s]]; Array[fxy,20] (* Harvey P. Dale, Aug 06 2020 *)
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003
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