login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A242877 Number of points of norm <= n in square lattice which can be built as entire powers of points of the square lattice seen as image of the complex plane C* (excluding (0,0)). 1
4, 6, 10, 12, 16, 20, 20, 24, 26, 30, 30, 42, 42, 46, 46, 48, 52, 52, 54, 58, 58, 58, 62, 62, 68, 70, 76, 76, 78, 80, 80, 92, 92, 96, 96, 98, 98, 102, 102, 106, 110, 110, 110, 110 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Martin Y. Champel, Table of n, a(n) for n = 1..10000

EXAMPLE

for n=1, a(1)=4 as (1,0),(0,1),(-1,0),(0,-1) are powers of (1,0), (0,-1),(0,1) and (0,1) respectively powered by 2,3,2 and 3.

for n=2, a(2)=6 as in addition of the 4 previous points can be found 2 points (0,2) and (0,-2) built as (1,1)^2 and (1,-1)^2.

for n=3, a(3)=10 as in addition of the 6 previous points can be found 4 points (2,2), (2,-2), (-2,-2) and (-2,2) built as (-1,1)^3, (-1,-1)^3, (1,-1)^3 and (1,1)^3 respectively.

PROG

(Python)

from math import *

i0=complex(1, 0)

i1=complex(0, 1)

f0={0, i0, i1, -i0, -i1}

def A242877(n):

....if n==0: return 0

....if n==1: return 4

....f0={0, i0, i1, -i0, -i1}

....k=2

....while True:

........ro=n**(1/k)

........if ro<sqrt(1.9999):break

........ro_int = int(ro)

........for a in range(-ro_int, ro_int+1):

............b_max = int(sqrt(ro*ro-a*a))

............for b in range(-b_max, b_max+1):

................c=complex(a, b)

................f0.add(c**k)

........k+=1

....return len(f0)-1

CROSSREFS

Cf. A000328, A001597, A069623.

Sequence in context: A156037 A089079 A310579 * A193948 A292794 A108724

Adjacent sequences:  A242874 A242875 A242876 * A242878 A242879 A242880

KEYWORD

nonn

AUTHOR

Martin Y. Champel, May 25 2014

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 2 11:35 EDT 2020. Contains 334771 sequences. (Running on oeis4.)