A393248 - OEIS

%I #16 Feb 16 2026 23:05:54

%S 1,1,1,3,3,3,1,1,1,1,1,1,1,1,1,15,15,15,15,15,15,15,15,15,15,15,15,15,

%T 15,15,1,6,6,6,3,3,6,6,6,6,6,1,6,6,3,6,6,6,3,6,6,6,6,3,6,3,6,6,6,6,6,

%U 6,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7

%N a(n) is the period length of the Ducci sequence, where the initial vector consists of the binary digits of n.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ducci_sequence">Ducci sequence</a>.

%F Let A_k = {a(n) | 2^(k-1) <= n < 2^k}. Then max(A_k) = A038553(k) and #A_k = A111944(k). - _Andrei Zabolotskii_, Feb 14 2026

%e n = 6: 6_10 = 110_2, vectors are (1,1,0)-->(0,1,1)-->(1,0,1)-->(1,1,0) repeats after 3 steps, thus a(6) = 3.

%e n = 7: 7_10 = 111_2, vectors are (1,1,1)-->(0,0,0)-->(0,0,0) repeats after 1 step, thus a(7) = 1.

%t a[n_] := Length[#] - FirstPosition[#, Last[#]][[1]]& @ NestWhileList[Abs[# - RotateLeft[#]] &, IntegerDigits[n, 2], Unequal, All]; Array[a, 80] (* _Amiram Eldar_, Feb 07 2026 *)

%Y Cf. A007788, A038553, A111944.

%K nonn,base

%O 1,4

%A _Ctibor O. Zizka_, Feb 07 2026