login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A010900 Pisot sequence E(4,13): a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

Satisfies a linear recurrence of order 6 just for n <= 23 (see A274952). - N. J. A. Sloane, Aug 07 2016

REFERENCES

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).

Ch. Pisot, "La répartition modulo un et les nombres algébriques", Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 7 : 2 (1938) pp. 205-248.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

David Cantor, Investigation of T-numbers and E-sequences, In Computers in Number Theory, ed. A. O. L. Atkin and B. J. Birch, Acad. Press, NY (1971); pp. 137-140. [Annotated scanned copy]

FORMULA

It is known that this does not satisfy any linear recurrence [Boyd].

PROG

(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

}

pisotE(50, 4, 13) \\ Colin Barker, Jul 28 2016

CROSSREFS

Cf. A007698, A007699, A010916, A274952.

See A008776 for definitions of Pisot sequences.

Sequence in context: A010919 A277667 A274952 * A175005 A070031 A082989

Adjacent sequences:  A010897 A010898 A010899 * A010901 A010902 A010903

KEYWORD

nonn

AUTHOR

Simon Plouffe

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 21 22:32 EST 2017. Contains 295054 sequences.