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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Fermat's 4n+1 theorem, sometimes called Fermat's two-square 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: Springer-Verlag, pp. 146-147 and 220-223, 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: Springer-Verlag, pp. 18-19, 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

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)