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A082981
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Start with the sequence S(0)={1,1} and for k>0 define S(k) to be I(S(k-1)) where I denotes the operation of inserting, for i=1,2,3..., the term a(i)+a(i+1) between any two terms for which 4a(i+1)<=5a(i). The listed terms are the initial terms of the limit of this process as k goes to infinity.
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4
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1, 2, 3, 4, 9, 14, 19, 24, 53, 82, 111, 140, 309, 478, 647, 816, 1801, 2786, 3771, 4756, 10497, 16238, 21979, 27720, 61181, 94642, 128103, 161564, 356589, 551614, 746639, 941664, 2078353, 3215042, 4351731, 5488420, 12113529, 18738638, 25363747
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Conjectures: (1) the section (a(2n+1)}={1,3,9,19,53,111,...} is A077442, the terms of which are solutions of ax^2+7 = a square, (2) the section {a(4n+1)}={1,9,53,309,1801,...} is A038761, (3) the section {a(4n+2)}={2,14,82,478,2786,...} is A077444, the terms of which are solutions of 2x^2+8 = a square, (4) the sequence {a(4n+2)/2}={1,7,41,239,1393,...} is A002315, the terms of which are solutions of 2x^2+2 = a square, (5) the section {a(4n+4)}={4,24,140,816,4756,...} is A005319, the terms of which are solutions of 2x^2+4=a square, (6) the sequence {a(4n+4)/4}={1,6,35,204,1189,...} is A001109, the terms of which are solutions of 8x^2+1=a square.
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FORMULA
| It appears that a(n)=6a(n-4)-a(n-8).
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CROSSREFS
| Cf. A001109, A002315, A005319, A038761, A077442 and A077444.
Sequence in context: A134313 A188531 A181287 * A077906 A133993 A122974
Adjacent sequences: A082978 A082979 A082980 * A082982 A082983 A082984
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), May 28 2003
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