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A118011
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Complement of the Connell sequence (A001614); a(n) = 4*n - A001614(n).
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7
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3, 6, 8, 11, 13, 15, 18, 20, 22, 24, 27, 29, 31, 33, 35, 38, 40, 42, 44, 46, 48, 51, 53, 55, 57, 59, 61, 63, 66, 68, 70, 72, 74, 76, 78, 80, 83, 85, 87, 89, 91, 93, 95, 97, 99, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 123, 125, 127, 129, 131, 133, 135, 137, 139
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OFFSET
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1,1
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COMMENTS
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a(n) is the position of the second appearance of n in A117384, where A117384(m) = A117384(k) and k = 4*A117384(m) - m. The Connell sequence (A001614) is generated as: 1 odd, 2 even, 3 odd, ...
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LINKS
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FORMULA
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a(n) = 2*n + 1 + Sum(j=0 .. n-2, A023531(j)).
G.f. 2*x/(1-x)^2 + x/(1-x) * Sum(j=0..infinity, x^(j*(j+1)/2))
= 2*x/(1-x)^2 + x^(7/8)/(2-2*x) * Theta2(0,sqrt(x)), where Theta2 is a Jacobi theta function. (End)
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MATHEMATICA
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PROG
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(Python)
from math import isqrt
def A118011(n): return (m:=n<<1)+(k:=isqrt(m))+int((m<<2)>(k<<2)*(k+1)+1) # Chai Wah Wu, Jul 26 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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