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

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.

Example

S(1) = 0 by definition; so a(1) = 0.
S(1)+1 = 1 has not yet occurred; so S(2) = 1 and a(2) = 1.
S(1)*(i+i) = 0 has already occurred.
S(2)+1 = 2 has not yet occurred; so S(3) = 2 and a(3) = 4.
S(2)*(1+i) = 1+i has not yet occured; so S(4) = 1+i and a(4) = 2.
S(3)+1 = 3 has not yet occurred; so S(5) = 3 and a(5) = 9.

Prog

(PARI) See Links section.

Crossrefs

Cf. A290536, A290537.

Sequence in context: A278103 A249327 A182728 * A097664 A144811 A185654

Adjacent sequences: A290535 A290536 A290537 * A290539 A290540 A290541

Keyword

nonn,look

Author

Rémy Sigrist, Aug 05 2017

Status

approved