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

1,2

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.

Links

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

Example

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).

Crossrefs

Cf. A374602, A377291.

Sequence in context: A009279 A059943 A264695 * A112336 A028390 A036500

Adjacent sequences: A377287 A377288 A377289 * A377291 A377292 A377293

Keyword

nonn

Author

Charles L. Hohn, Oct 23 2024

Status

approved