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A072987
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FIBMOD numbers: a(1) = a(2) = 1, a(n) = a(n-1) mod (n-1) + a(n-2) mod (n-2).
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3
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1, 1, 1, 2, 3, 5, 8, 6, 7, 13, 10, 13, 11, 12, 23, 20, 12, 16, 28, 25, 14, 19, 33, 29, 15, 20, 35, 28, 8, 8, 16, 24, 40, 31, 38, 34, 37, 34, 34, 68, 62, 49, 28, 35, 63, 53, 25, 32, 57, 40, 48, 88, 84, 67, 44, 57, 45, 46, 91, 78, 50, 68, 56, 62, 118, 115, 102
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OFFSET
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1,4
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COMMENTS
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Superseeker suggested that this sequence might be related to A096534 via the transformation T026 (coefficients of Sn(z)/(1+z)) for a(3) to a(76). - Eli Jaffe, Sep 16 2015
Superseeker's reply seems to be true: it appears that the present sequence has generating function equal to (1+x)*(1+x*G(X)), where G(x) is the g.f. for A096534. - N. J. A. Sloane, Nov 23 2015
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LINKS
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FORMULA
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a(n) < 2n.
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EXAMPLE
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For n=8, a(8) = (a(7) mod 7) + (a(6) mod 6) = 1 + 5 = 6. - Eli Jaffe, Sep 16 2015
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MAPLE
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a:= proc(n) option remember; `if`(n<3, 1,
add(irem(a(n-j), n-j), j=1..2))
end:
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MATHEMATICA
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a = {1, 1}; Do[AppendTo[a, Mod[a[[n - 1]], n - 1] + Mod[a[[n - 2]], n - 2]], {n, 3, 76}]; a (* Michael De Vlieger, Sep 17 2015 *)
RecurrenceTable[{a[1]==a[2]==1, a[n]==Mod[a[n-1], n-1]+Mod[a[n-2], n-2]}, a, {n, 80}] (* Harvey P. Dale, Oct 28 2017 *)
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PROG
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(Magma) I:=[1, 1]; [n le 2 select I[n] else Self(n-1) mod (n-1) + Self(n-2) mod (n-2): n in [1..80]]; // Vincenzo Librandi, Sep 26 2015
(PARI) a=vector(10^5); a[1]=a[2]=1; for(n=3, #a, a[n]=a[n-1]%(n-1)+a[n-2]%(n-2)); a \\ Altug Alkan, Mar 20 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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