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Search: id:A109748
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| A109748 |
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Integers n such that n is prime and x is prime, where (x,y) is the smallest solution to the Pell equation with D = n. |
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2
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| 2, 3, 37, 73, 97, 577, 757, 997, 1297, 4357, 5197, 7213, 7873, 8737, 8761, 10273, 13033, 18097, 23041, 23593, 24169, 24337, 24697, 26713, 29437, 37117, 41257, 41617, 43117, 45817, 46573, 49033, 49201, 49393, 56857, 57601, 59341, 60601
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OFFSET
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1,1
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REFERENCES
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Beiler, A. H. "The Pellian." Ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. New York: Dover, pp. 248-268, 1966.
Cohn, H. "Pell's Equation." Sect. 6.9 in Advanced Number Theory. New York: Dover, pp. 110-111, 1980.
Cox, D. A. Primes of the form x^2 + ny^2. New York: Wiley, 1989.
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LINKS
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Eric Weisstein's World of Mathematics, Pell Equation
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FORMULA
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n prime and x prime, where (x, y) is the smallest solution to the Pell equation x^2 - n*(y^2) = 1.
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EXAMPLE
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a(1) = 2 because 2 is prime, 3 is prime, and (3,2) is the smallest x,y solution such that x^2 - 2*(y^2) = 1.
a(2) = 3 because 3 is prime, 2 is prime and (2,1) is the smallest x,y solution such that x^2 - 3*(y^2) = 1.
a(3) = 37 because 37 is prime, 73 is prime and (73,12) is the smallest x,y solution such that x^2 - 37*(y^2) = 1.
a(4) = 73 because 73 is prime, 2281249 is prime and (2281249,267000) is the smallest x,y solution such that x^2 - 73*(y^2) = 1.
a(5) = 97 because 97 is prime, 62809633 is prime and (62809633,6377352) is the smallest x,y solution such that x^2 - 97*(y^2) = 1.
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CROSSREFS
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Cf. A062326 (for the case of n and y both prime).
Sequence in context: A080357 A064032 A118443 this_sequence A062459 A118370 A061576
Adjacent sequences: A109745 A109746 A109747 this_sequence A109749 A109750 A109751
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Aug 10 2005
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), May 17 2007
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