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A055500
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a(0)=1, a(1)=1, a(n) = largest prime <= a(n-1)+a(n-2).
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7
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1, 1, 2, 3, 5, 7, 11, 17, 23, 37, 59, 89, 139, 227, 359, 577, 929, 1499, 2423, 3919, 6337, 10253, 16573, 26821, 43391, 70207, 113591, 183797, 297377, 481171, 778541, 1259701, 2038217, 3297913, 5336129, 8633983, 13970093, 22604069
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Might be called the Prime-Fibonacci sequence. - Bodo Zinser (BodoZinser(AT)Compuserve.com), Nov 17 2001
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LINKS
| Zak Seidov, Table of n, a(n) for n = 0..100.
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FORMULA
| a(n) is asymptotic to C*phi^n where phi=(1+sqrt(5))/2 and C=0.25861637901860700965101922576495456677... - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
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EXAMPLE
| a(9) = 23 because 23 is largest prime <= a(7)+a(6) = 17+11 = 28
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MATHEMATICA
| PrevPrim[n_] := Block[ {k = n}, While[ !PrimeQ[k], k-- ]; Return[k]]; a[1] = a[2] = 1; a[n_] := a[n] = PrevPrim[ a[n - 1] + a[n - 2]]; Table[ a[n], {n, 1, 42} ]
(* Or, if version >= 6 : *)a[0] = a[1] = 1; a[n_] := a[n] = NextPrime[ a[n-1] + a[n-2] + 1, -1]; Table[a[n], {n, 0, 100}](* From Jean-François Alcover, Jan 12 2012 *)
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CROSSREFS
| Cf. A055498-A055502, A065435, A000045.
Sequence in context: A104892 A065436 A068523 * A018058 A002379 A072465
Adjacent sequences: A055497 A055498 A055499 * A055501 A055502 A055503
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 08 2000
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