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A365203 a(1) = 1; a(n) = a(n - 1) + n if a(n - 1) < n, a(n) = n^2 if a(n - 1) = n, a(n) = a(n - 1)/n if a(n - 1) > n and a(n - 1) == 0 (mod n), otherwise a(n) = a(n - 1) - n.

%I A365203 #42 Apr 30 2025 12:23:05
%S A365203 1,3,9,5,25,19,12,4,13,3,14,2,15,1,16,256,239,221,202,182,161,139,116,
%T A365203 92,67,41,14,42,13,43,12,44,11,45,10,46,9,47,8,48,7,49,6,50,5,51,4,52,
%U A365203 3,53,2,54,1,55,3025,2969,2912,2854,2795,2735,2674,2612,2549
%N A365203 a(1) = 1; a(n) = a(n - 1) + n if a(n - 1) < n, a(n) = n^2 if a(n - 1) = n, a(n) = a(n - 1)/n if a(n - 1) > n and a(n - 1) == 0 (mod n), otherwise a(n) = a(n - 1) - n.
%H A365203 Felix Huber, <a href="/A365203/b365203.txt">Table of n, a(n) for n = 1..10000</a>
%e A365203 a(2) = a(1) + 2 = 3, since a(1) = 1 < 2.
%e A365203 a(3) = 3^2 = 9, since a(2) = 2.
%e A365203 a(4) = a(3) - 4 = 5, since a(3) = 9 > 4 and 9 != 0 (mod 4).
%e A365203 a(83) = a(82)/83 = 14, a(82) = 1162 > 83 and 1162 == 0 (mod 83).
%p A365203 A365203 := proc(n) option remember;
%p A365203     if n = 1 then 1;
%p A365203     elif procname(n - 1) < n then procname(n - 1) + n;
%p A365203     elif n = procname(n - 1) then n*n;
%p A365203     elif irem(procname(n - 1), n) = 0 then procname(n - 1)/n;
%p A365203     else procname(n - 1) - n;
%p A365203     end if;
%p A365203 end proc;
%p A365203 seq(A365203(n), n = 1 .. 10000);
%t A365203 nxt[{n_,a_}]:={n+1,Which[a<(n+1),a+n+1,a==n+1,(n+1)^2,a>(n+1)&&Mod[a,n+1]==0,a/(n+1),True,a-n-1]}; NestList[nxt,{1,1},70][[;;,2]] (* _Harvey P. Dale_, Apr 30 2025 *)
%o A365203 (PARI) lista(nn) = my(va = vector(nn)); va[1] = 1; for (n=2, nn, my(vs = sign(va[n-1] - n)); if (vs<0, va[n] = va[n-1] + n, if (vs==0, va[n] = n^2, if ((va[n-1] % n)== 0, va[n] = va[n-1]/n, va[n] = va[n-1] - n)));); va; \\ _Michel Marcus_, Aug 27 2023
%o A365203 (Python)
%o A365203 from itertools import count, islice
%o A365203 def A365203_gen(): # generator of terms
%o A365203     yield (a:=1)
%o A365203     for n in count(2):
%o A365203         if a<n:
%o A365203             b = a+n
%o A365203         elif a==n:
%o A365203             b = n**2
%o A365203         elif a%n:
%o A365203             b = a-n
%o A365203         else:
%o A365203             b = a//n
%o A365203         yield (a:=b)
%o A365203 A365203_list = list(islice(A365203_gen(),30)) # _Chai Wah Wu_, Sep 23 2023
%Y A365203 Cf. A000290, A046901.
%K A365203 easy,nonn
%O A365203 1,2
%A A365203 _Felix Huber_, Aug 26 2023