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A010900
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Pisot sequence E(4,13): a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
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3
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4, 13, 42, 136, 440, 1424, 4609, 14918, 48285, 156284, 505844, 1637264, 5299328, 17152321, 55516872, 179691313, 581606398, 1882483892, 6093030640, 19721296176, 63831867233, 206604436042, 668716032329, 2164431415224, 7005609443657, 22675037578854
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OFFSET
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0,1
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COMMENTS
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According to David Boyd his last use (as of April, 2006) of his Pisot number finding program was to prove that in fact this sequence does not satisfy a linear recurrence. He remarks "This took a couple of years in background on various Sun workstations." - Gene Ward Smith, Apr 11 2006
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REFERENCES
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Cantor, D. G. "Investigation of T-numbers and E-sequences." In Computers in Number Theory, ed. AOL Atkin and BJ Birch, Acad. Press, NY (1971); pp. 137-140.
Cantor, D. G. (1976). On families of Pisot E-sequences. In Annales scientifiques de l'École Normale Supérieure (Vol. 9, No. 2, pp. 283-308).
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LINKS
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FORMULA
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It is known that this does not satisfy any linear recurrence [Boyd].
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MATHEMATICA
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nxt[{a_, b_}]:={b, Floor[b^2/a+1/2]}; NestList[nxt, {4, 13}, 30][[All, 1]] (* Harvey P. Dale, Jun 24 2018 *)
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PROG
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(PARI) pisotE(nmax, a1, a2) = {
a=vector(nmax); a[1]=a1; a[2]=a2;
for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));
a
}
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CROSSREFS
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See A008776 for definitions of Pisot sequences.
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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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