A377290 For each row n in array A374602(n, k), the period size, as a count of terms, that divides the row into congruent subsequences.

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, 14, 18, 16, 12, 38, 22, 28, 26, 42, 20, 74, 36, 14, 54, 12, 16, 34, 38, 54, 26, 58, 50, 24, 36, 102, 46, 32, 78, 14, 22, 38, 46, 118, 22, 30, 68, 36, 32, 130, 74, 34

Offset: 1

Author

Charles L. Hohn, Oct 23 2024

Keywords

• nonn

Comments

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.

Examples

			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:
sqrt((7-3)*1^2 + 3*(1+1)^2) = 4,
sqrt((7-6)*1^2 + 6*(1+1)^2) = 5,
sqrt((7-1)*4^2 + 1*(4+1)^2) = 11,
sqrt((7-4)*10^2 + 4*(10+1)^2) = 28,
sqrt((7-3)*23^2 + 3*(23+1)^2) = 62,
sqrt((7-6)*29^2 + 6*(29+1)^2) = 79,
sqrt((7-1)*66^2 + 1*(66+1)^2) = 175,
sqrt((7-4)*168^2 + 4*(168+1)^2) = 446,
producing the repeating pattern of c values {3, 6, 1, 4}, of length 4 -> a(5).
		

Links

• Charles L. Hohn, Table of n, a(n) for n = 1..90

Crossrefs

Cf. A374602, A377291.