OFFSET
1,2
COMMENTS
Numbers of the form x^2 + y^2 with gcd(x, y) = 1 that have no other decompositions into a sum of two squares.
Numbers 1 and 2 together with p and 2p, where prime p == 1 (mod 4).
Conjecture: each positive integer is a sum |x| + |y| such that x^2 + y^2 is in the sequence.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ C n log n, where C = 4/3. - Charles R Greathouse IV, Feb 01 2017, corrected by Thomas Ordowski, Feb 10 2017
EXAMPLE
1 = 0^2 + 1^2 and 2 = 1^1 + 1^2.
p = x^2 + y^2 and 2p = (y-x)^2 + (x+y)^2.
PROG
(PARI) is(n)=if(n<5, n==1 || n==2, if(n%2==0, n/=2); n%4==1 && isprime(n)) \\ Charles R Greathouse IV, Feb 01 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thomas Ordowski, Jan 19 2017
STATUS
approved