

A107961


Pythagorean semiprimes: products of two Pythagorean primes (A002313).


0



4, 10, 25, 26, 34, 58, 65, 74, 82, 85, 106, 122, 145, 146, 169, 178, 185, 194, 202, 205, 218, 221, 226, 265, 274, 289, 298, 305, 314, 346, 362, 365, 377, 386, 394, 445, 458, 466, 481, 482, 485, 493, 505, 514, 533, 538, 545, 554, 562, 565, 586, 626, 629, 634
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OFFSET

1,1


COMMENTS

Fermat's 4n+1 theorem, sometimes called Fermat's twosquare theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique manner (up to the order of addends) in the form x^2 + y^2 for integer x and y iff p = 1 (mod 4) or p = 2 (which is a degenerate case with x = y = 1). The theorem was stated by Fermat, but the first published proof was by Euler.


REFERENCES

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: SpringerVerlag, pp. 146147 and 220223, 1996.
Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 13 and 219, 1979.
Seroul, R. "Prime Number and Sum of Two Squares." Section 2.11 in Programming for Mathematicians. Berlin: SpringerVerlag, pp. 1819, 2000.


LINKS

Table of n, a(n) for n=1..54.
Eric Weisstein's World of Mathematics, Fermat's 4n Plus 1 Theorem.
Eric Weisstein's World of Mathematics, Semiprime.


FORMULA

{a(n)} = {p*q: p and q both elements of A002313} = {p*q: p and q both of form m^2 + n^2 for integers m, n}.


CROSSREFS

Cf. A001358, A002313, A002330, A002331.
Sequence in context: A223014 A038783 A127070 * A051864 A111153 A265438
Adjacent sequences: A107958 A107959 A107960 * A107962 A107963 A107964


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jun 12 2005


STATUS

approved



