The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 30 05:35 EDT 2020. Contains 334712 sequences. (Running on oeis4.)