A377290 - OEIS

%I #7 Nov 15 2024 23:31:49

%S 1,2,2,6,4,4,14,10,8,10,6,8,14,16,34,10,8,34,8,12,22,22,32,18,18,30,

%T 14,18,16,12,38,22,28,26,42,20,74,36,14,54,12,16,34,38,54,26,58,50,24,

%U 36,102,46,32,78,14,22,38,46,118,22,30,68,36,32,130,74,34

%N For each row n in array A374602(n, k), the period size, as a count of terms, that divides the row into congruent subsequences.

%C Here "congruent" means: 1) In the defining formula of A374602: sqrt((d-c)*b^2 + c*(b+1)^2), A374602(n, k) and A374602(n, k+a(n)) have equal c values (see Example), and also 2) A374602(n, k+a(n))/A374602(n, k) converges to a limit as k->oo, shown in A377291.

%H Charles L. Hohn, <a href="/A377290/b377290.txt">Table of n, a(n) for n = 1..90</a>

%e Given formula sqrt((d-c)*b^2 + c*(b+1)^2) from A374602, for n=5, the first few terms of A374602(5, k) are:

%e sqrt((7-3)*1^2 + 3*(1+1)^2) = 4,

%e sqrt((7-6)*1^2 + 6*(1+1)^2) = 5,

%e sqrt((7-1)*4^2 + 1*(4+1)^2) = 11,

%e sqrt((7-4)*10^2 + 4*(10+1)^2) = 28,

%e sqrt((7-3)*23^2 + 3*(23+1)^2) = 62,

%e sqrt((7-6)*29^2 + 6*(29+1)^2) = 79,

%e sqrt((7-1)*66^2 + 1*(66+1)^2) = 175,

%e sqrt((7-4)*168^2 + 4*(168+1)^2) = 446,

%e producing the repeating pattern of c values {3, 6, 1, 4}, of length 4 -> a(5).

%Y Cf. A374602, A377291.

%K nonn

%O 1,2

%A _Charles L. Hohn_, Oct 23 2024