A290538 - OEIS

A290538

Let S be the sequence generated by these rules: 0 is in S, and if z is in S, then z + 1 and z * (1+i) are in S (where i denotes the imaginary unit), and duplicates are deleted as they occur; a(n) = the square of the norm of the n-th term of S.

0, 1, 4, 2, 9, 8, 5, 4, 16, 18, 13, 16, 10, 10, 5, 8, 25, 32, 25, 36, 20, 26, 17, 32, 17, 20, 13, 20, 10, 5, 16, 36, 50, 41, 64, 34, 50, 37, 72, 29, 40, 29, 52, 34, 25, 64, 26, 34, 25, 40, 26, 17, 40, 9, 20, 10, 9, 32, 49, 72, 61, 100, 52, 82, 65, 128, 45, 68

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

See A290536 for the real part of the n-th term of S and additional comments.

See A290537 for the imaginary part of the n-th term of S.

a(n) tends to infinity as n tends to infinity.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A290538

FORMULA

a(n) = A290536(n)^2 + A290537(n)^2.