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A319561 Let f(1) = 1, f(2) = 1 + i (where i denotes the imaginary unit), and for n > 1, f(n+1) is the Gaussian integer in the first quadrant (with positive real part and nonnegative imaginary part) with least modulus and sharing a prime factor with f(n) (in case of a tie, minimize the imaginary part); a(n) = the square of the modulus of f(n). 4
1, 2, 4, 8, 10, 5, 20, 10, 5, 20, 16, 18, 9, 36, 26, 13, 52, 26, 13, 52, 32, 34, 17, 68, 34, 17, 68, 40, 25, 25, 45, 45, 25, 40, 50, 50, 50, 58, 29, 116, 58, 29, 116, 64, 72, 74, 37, 148, 74, 37, 148, 80, 65, 65, 65, 65, 85, 85, 85, 80, 82, 41, 164, 82, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The real and imaginary parts of f are respectively given by A319562 and A319563.

The sequence f is a complex variant of the EKG sequence (A064413).

This sequence and A064413 have similar graphical features.

Apparently, the sequence f runs through all Gaussian integers in the first quadrant.

LINKS

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

Rémy Sigrist, PARI program for A319561

Rémy Sigrist, Representation of f(n) in the complex plane for n = 1..100000

FORMULA

a(n) = A319562(n)^2 + A319563(n)^2.

EXAMPLE

The first terms, alongside f(n) and gcd(f(n), f(n+1)), are:

  n  a(n)    f(n)       gcd(f(n), f(n+1))

  -- ----    ----       -----------------

   1    1    1          1

   2    2    1 + i      1 + i

   3    4    2          2

   4    8    2 + 2*i    1 + i

   5   10    3 + i      1 + 2*i

   6    5    1 + 2*i    1 + 2*i

   7   20    2 + 4*i    1 + i

   8   10    1 + 3*i    2 + i

   9    5    2 + i      2 + i

  10   20    4 + 2*i    2

  11   16    4          1 + i

  12   18    3 + 3*i    3

  13    9    3          3

  14   36    6          1 + i

  15   26    5 + i      2 + 3*i

PROG

(PARI) See Links section.

CROSSREFS

Cf. A064413, A319562, A319563.

Sequence in context: A028984 A294369 A302907 * A153181 A256624 A247324

Adjacent sequences:  A319558 A319559 A319560 * A319562 A319563 A319564

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Sep 23 2018

STATUS

approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)