A087877 Primes of the form (4n+1)^2 + (4m)^2, m,n = 0,1,2..

17, 41, 89, 97, 233, 257, 281, 313, 337, 353, 401, 433, 457, 569, 577, 601, 641, 769, 809, 857, 881, 953, 1049, 1097, 1153, 1193, 1201, 1297, 1321, 1409, 1433, 1489, 1601, 1697, 1873, 1889, 2017, 2081, 2089, 2113, 2137, 2153, 2281, 2377, 2393, 2417, 2441

Offset

1,1

Comments

If an odd number is of the form a^2 + b^2, then a and b must be one of the following forms.

a=4n+1, b=4m so that a^2+b^2 = 16(m^2+n^2) + 8n + 1 of form 4k1+1

a=4n+3, b=4m a^2+b^2 = 16(m^2+n^2) + 24n + 1 of form 4k2+1

a=4n+1, b=4m+2 a^2+b^2 = 16(m^2+n^2) + 8(n+2m ) + 5 of form 4k3+1

a=4n+3, b=4m+2 a^2+b^2 = 16(m^2+n^2) + 8(3n+2m) + 13 of form 4k4+1

The sequences built using these 4 forms produce all prime numbers of the form 4k+1.This particular sequence is a=4n+1, b=4m.

Links

Table of n, a(n) for n=1..47.

Crossrefs

Sequence in context: A054819 A235743 A299797 * A107181 A158014 A139879

Adjacent sequences: A087874 A087875 A087876 * A087878 A087879 A087880

Keyword

nonn

Author

Cino Hilliard, Oct 11 2003

Status

approved