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A059923
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a(n+1) is smallest number with a(n+1)^n > a(n)^(n+1).
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3
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1, 2, 3, 5, 8, 13, 20, 31, 48, 74, 114, 176, 271, 417, 642, 988, 1521, 2341, 3603, 5545, 8533, 13131, 20207, 31096, 47853, 73639, 113320, 174383, 268350, 412951, 635471, 977896, 1504837, 2315721, 3563551, 5483776, 8438716, 12985930, 19983416
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A kind of discrete exponential, since the series of n-th differences resembles the original sequence. The principle of construction is F(a(n+1)) > G(a(n)) as in A059842 but slightly modified to F(n,a(n+1)) > F(n+1,a(n)) with F(n,x) = x^n. This seems to be a fruitful construction principle!
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..300
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FORMULA
| a(n+1) = floor( a(n)^(1+1/n) ) + 1; compare A080870. - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 21 2003
a(n) = floor(x^n), where x=1.53885131519173... - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 21 2003
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EXAMPLE
| We have a(5)=8 and therefore a(6) = 13 because 13^5 > 8^6.
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MAPLE
| a := proc(n) option remember: if n=1 then RETURN(1) fi: if n=2 then RETURN(2) fi: ceil(a(n-1)^((n)/(n-1))): end: Digits := 20: for n from 1 to 250 do printf(`%d, `, a(n)) od:
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PROG
| (PARI) { default(realprecision, 200); a=1; for (n=1, 300, write("b059923.txt", n, " ", a); a=floor(a^(1 + 1/n)) + 1; ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 30 2009]
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CROSSREFS
| Cf. A059842, A080869, A080870.
Sequence in context: A088795 A156145 A173597 * A055805 A023437 A013985
Adjacent sequences: A059920 A059921 A059922 * A059924 A059925 A059926
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Rainer Rosenthal (r.rosenthal(AT)web.de), Mar 03 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Mar 15 2001
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