The On-Line Encyclopedia of Integer Sequences (OEIS)

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A018907

Define the sequence S(a_0,a_1) by a_{n+2} is the least integer such that a_{n+2}/a_{n+1} > a_{n+1}/a_n for n >= 0. This is S(2,7).
(history; published version)

#23 by Ray Chandler at Thu Jul 13 09:25:42 EDT 2023

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#22 by Ray Chandler at Thu Jul 13 09:25:39 EDT 2023

LINKS

<a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>

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#21 by Alois P. Heinz at Mon Nov 16 12:09:11 EST 2020

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#20 by Jean-François Alcover at Mon Nov 16 11:33:48 EST 2020

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#19 by Jean-François Alcover at Mon Nov 16 11:33:42 EST 2020

MATHEMATICA

a[n_] := a[n] = Switch[n, 0, 2, 1, 7, _, 1 + Floor[a[n-1]^2/a[n-2]]];

a /@ Range[0, 40] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

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#18 by R. J. Mathar at Tue Mar 22 12:30:59 EDT 2016

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#17 by R. J. Mathar at Tue Mar 22 12:30:43 EDT 2016

REFERENCES

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

LINKS

D. W. Boyd, <a href="https://www.researchgate.net/profile/David_Boyd7/publication/262181133_Linear_recurrence_relations_for_some_generalized_Pisot_sequences_-_annotated_with_corrections_and_additions/links/00b7d536d49781037f000000.pdf">Linear recurrence relations for some generalized Pisot sequences</a>, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

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#16 by Alois P. Heinz at Tue Feb 16 08:35:14 EST 2016

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#15 by Colin Barker at Tue Feb 16 08:34:07 EST 2016

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#14 by Colin Barker at Tue Feb 16 08:33:59 EST 2016

PROG

(PARI) S(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=a[n-1]^2\a[n-2]+1); a

S(2, 7, 40) \\ Colin Barker, Feb 16 2016

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editing