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A005041
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A self-generating sequence.
(Formerly M0258)
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3
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1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Jeffrey Shallit, Letter to N. J. A. Sloane, Nov 10 1979. Attached: James Propp, Problem 1047, Math. Mag., 52 (1979), 265. [Annotated scanned copy]
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FORMULA
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For any k in {0, 1, 2, ...} and r in {0, 1, 2), we have: if n = 6*k + (3/2)*k*(k-1) + r*(k+2), then a(n) = 3*k + r + 1. E.g., for k=3 and r=1, we have n = 6*3 + (3/2)*3*(3-1) + 1*(3+2) = 32 and so a(32) = 3*3 + 1 + 1 = 11. - Francois Jooste (phukraut(AT)hotmail.com), Mar 12 2002
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MATHEMATICA
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PROG
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(Haskell)
a005041 n = a005041_list !! n
a005041_list = 1 : f 1 1 (tail ts) where
f y i gs'@((j, a):gs) | i < j = y : f y (i+1) gs'
| i == j = a : f a (i+1) gs
ts = [(6*k + 3*k*(k-1) `div` 2 + r*(k+2), 3*k+r+1) |
k <- [0..], r <- [0, 1, 2]]
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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More terms from Samuel Hilliard (sam_spade1977(AT)hotmail.com), Apr 11 2004
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STATUS
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approved
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