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A268176 a(0) = a(1) = 1, and a(n) = a(n-1) + a( (a(n-1)-1) mod n ) for n>=2.

%I A268176 #31 Jun 17 2021 06:11:30
%S A268176 1,1,2,3,5,10,13,23,36,72,73,86,87,123,196,197,202,398,399,798,1196,
%T A268176 1994,2117,2118,2128,2130,4248,4284,8568,8655,8851,9048,11166,11252,
%U A268176 20300,40600,44884,44886,44909,45707,49955,50157,50193,50279,59130,118260,163967
%N A268176 a(0) = a(1) = 1, and a(n) = a(n-1) + a( (a(n-1)-1) mod n ) for n>=2.
%H A268176 Alois P. Heinz, <a href="/A268176/b268176.txt">Table of n, a(n) for n = 0..10000</a>
%H A268176 N. J. A. Sloane, <a href="/A268176/a268176.pdf">Open Problems in the OEIS</a>, Slides of Guest Lecture given in Doron Zeilberger's Experimental Mathematics Class, Rutgers University, May 2, 2016.
%p A268176 a:= proc(n) option remember; `if`(n<2, 1,
%p A268176        a(n-1)+a(irem((a(n-1)-1), n)))
%p A268176     end:
%p A268176 seq(a(n), n=0..50);  # _Alois P. Heinz_, Apr 08 2016
%t A268176 a[0] = a[1] = 1; a[n_] := a[n] = # + a@ Mod[# - 1, n] &@ a[n - 1]; Array[a, 47, 0] (* _Michael De Vlieger_, Apr 08 2016 *)
%o A268176 (PARI) lista(nn) = {va = vector(nn); print1(va[1] = 1, ", "); print1(va[2] = 1, ", "); for (n=3, nn, va[n] = va[n-1] + va[((va[n-1]-1) % (n-1))+1]; print1(va[n], ", "););} \\ _Michel Marcus_, Apr 08 2016
%o A268176 (Python)
%o A268176 from sympy.core.cache import cacheit
%o A268176 @cacheit
%o A268176 def a(n): return 1 if n<2 else a(n - 1) + a((a(n - 1) - 1)%n)
%o A268176 print([a(n) for n in range(51)]) # _Indranil Ghosh_, Aug 06 2017
%Y A268176 Cf. A125204.
%K A268176 nonn,easy
%O A268176 0,3
%A A268176 _Christian Perfect_, Jan 28 2016