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A006695
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a(2n)=2*a(2n-2)^2-1, a(2n+1)=2a(2n)-1, a(0)=2.
(Formerly M0838)
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2
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2, 3, 7, 13, 97, 193, 18817, 37633, 708158977, 1416317953, 1002978273411373057, 2005956546822746113, 2011930833870518011412817828051050497, 4023861667741036022825635656102100993
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| An infinite coprime sequence defined by recursion.
Every term is relatively prime to all others. - Michael Somos Feb 01 2004
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REFERENCES
| S. Kalpazidou et al., Luroth [ Lueroth ]-type alternating series representations for real numbers, Acta Arithmetica, 55 (1990), 311-322.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..19
J. O. Shallit, Rational numbers with non-terminating, non-periodic modified Engel-type expansions, Fib. Quart., 31 (1993), 37-40.
Index entries for sequences related to Engel expansions
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PROG
| (PARI) a(n)=if(n<1, 2*(n==0), if(n%2, 2*a(n-1)-1, 2*a(n-2)^2-1))
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CROSSREFS
| a(2n)=A001075(2^n).
Cf. A001685, A002715, A003686, A064526.
Sequence in context: A078154 A192611 A048463 * A128157 A073827 A081940
Adjacent sequences: A006692 A006693 A006694 * A006696 A006697 A006698
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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