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A028392
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a(n) = n + floor(sqrt(n)).
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17
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0, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79
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OFFSET
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0,2
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COMMENTS
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Also the sequence of integers left after performing the following procedure:
1. Remove the element at 1st position (1) and compact the sequence;
2. Remove the element at 4th (2^2-th) position (5) and compact the sequence;
3. Remove the element at 9th (3^2-th) position (11) and compact the sequence;
....
n. Remove the element at (n-square)th position (n^2 + n - 1) and compact the sequence;
(End)
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LINKS
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FORMULA
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G.f.: x / (1 - x)^2 + (theta3(x) - 1) / (2 * (1 - x)). - Michael Somos, Mar 24 2012
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EXAMPLE
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G.f. = 2*x + 3*x^2 + 4*x^3 + 6*x^4 + 7*x^5 + 8*x^6 + 9*x^7 + 10*x^8 + 12*x^9 + ...
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MATHEMATICA
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PROG
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(PARI) {a(n) = if( n<0, 0, n + sqrtint(n))}; /* Michael Somos, Jun 11 2003 */
(Haskell)
(Scala) (0 to 99).map(n => (n + Math.floor(Math.sqrt(n))).toInt) // Alonso del Arte, Nov 03 2019
(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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