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A076116
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Start of the smallest string of n consecutive positive numbers with a cube sum, or 0 if no such number exists.
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2
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1, 13, 8, 0, 23, 2, 46, 0, 20, 8, 116, 0, 163, 18, 218, 6, 281, 32, 352, 0, 431, 50, 518, 0, 28, 72, 14, 0, 827, 98, 946, 0, 1073, 128, 1208, 0, 1351, 162, 1502, 0, 1661, 200, 1828, 0, 53, 242, 2186, 98, 32, 43, 2576, 0, 2783, 36, 2998, 0, 3221, 392, 3452, 0, 3691, 450
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OFFSET
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1,2
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LINKS
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FORMULA
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If n is odd, then a(n) is the least positive integer of the form (k*A019555(n))^3/n - (n-1)/2 where k is an integer.
If n is even, then let v = A007814(n). If v == 1 (mod 3) then a(n) is the least positive integer of the form (k*A019555(n/2))^3/n - (n-1)/2 where k an odd integer; otherwise, a(n) = 0. (End)
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MAPLE
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f:= proc(n) local y, F, t, k, v;
if n::odd then
F:= ifactors(n)[2];
y:= mul(t[1]^ceil(t[2]/3), t=F);
k:= 1+floor((n*(n-1)/2)^(1/3)/y);
(k*y)^3/n - (n-1)/2;
else
v:= padic:-ordp(n, 2);
if v mod 3 <> 1 then return 0 fi;
F:= ifactors(n/2^v)[2];
y:= mul(t[1]^ceil(t[2]/3), t=F)*2^((v-1)/3);
k:= 1 + floor((n*(n-1)/2)^(1/3)/y);
if k::even then k:= k+1 fi;
(k*y)^3/n - (n-1)/2;
fi
end proc:
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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