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a(1) = 1; for n > 1, a(n) is the smallest number > a(n-1) such that a(1) + a(2) + ... + a(n) is a composite number.
{a(n)} = {1, 3, 4, 6, 7} union {9, 10, 11, 12, ...} and the sum s(n) = a(1) + a(2) + ... + a(n) is always composite because s(1) = 1, s(2) = 4, s(3) = 8, s(4) = 14 and for n = 5,6,7,... s(n) = (n-2)*(n+9)/2 = 21, 30, 40, 51, ... = A056115(n) for n >= 3.
nonn,easy,changed
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<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
From Chai Wah Wu, Jan 28 2024: (Start)
a(n) = 2*a(n-1) - a(n-2) for n > 7.
G.f.: x*(-x^6 + x^5 - x^4 + x^3 - x^2 + x + 1)/(x - 1)^2. (End)
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Harvey P. Dale, <a href="/A233334/b233334_1.txt">Table of n, a(n) for n = 1..1000</a>
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Harvey P. Dale, <a href="/A233334/b233334_1.txt">Table of n, a(n) for n = 1..1000</a>
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