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.

1, 3, 9, 5, 25, 19, 12, 4, 13, 3, 14, 2, 15, 1, 16, 256, 239, 221, 202, 182, 161, 139, 116, 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, 3, 53, 2, 54, 1, 55, 3025, 2969, 2912, 2854, 2795, 2735, 2674, 2612, 2549

Offset: 1

Author

Felix Huber, Aug 26 2023

Keywords

• easy
• nonn

Examples

			a(2) = a(1) + 2 = 3, since a(1) = 1 < 2.
a(3) = 3^2 = 9, since a(2) = 2.
a(4) = a(3) - 4 = 5, since a(3) = 9 > 4 and 9 != 0 (mod 4).
a(83) = a(82)/83 = 14, a(82) = 1162 > 83 and 1162 == 0 (mod 83).
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A046901.

Programs

Maple

A365203 := proc(n) option remember;
    if n = 1 then 1;
    elif procname(n - 1) < n then procname(n - 1) + n;
    elif n = procname(n - 1) then n*n;
    elif irem(procname(n - 1), n) = 0 then procname(n - 1)/n;
    else procname(n - 1) - n;
    end if;
end proc;
seq(A365203(n), n = 1 .. 10000);

Mathematica

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 *)

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

Python

from itertools import count, islice
def A365203_gen(): # generator of terms
    yield (a:=1)
    for n in count(2):
        if aA365203_list = list(islice(A365203_gen(),30)) # Chai Wah Wu, Sep 23 2023