A072987 FIBMOD numbers: a(1) = a(2) = 1, a(n) = a(n-1) mod (n-1) + a(n-2) mod (n-2).

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

Offset: 1

Author

Benoit Cloitre, Aug 14 2002

Keywords

• easy
• nonn

Comments

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

Examples

			For n=8, a(8) = (a(7) mod 7) + (a(6) mod 6) = 1 + 5 = 6. - _Eli Jaffe_, Sep 16 2015
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A096534.

Programs

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

Maple

a:= proc(n) option remember; `if`(n<3, 1,
      add(irem(a(n-j), n-j), j=1..2))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 20 2018

Mathematica

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 *)

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

Formula

a(n) < 2n.

A096534(n) == a(n) mod n. - Danny Rorabaugh, Oct 13 2015

Extensions

Corrected by Harvey P. Dale, Oct 28 2017