OFFSET
1,1
COMMENTS
c^2 = b^2 + a^2 with c > b > a relatively prime, i.e. a primitive Pythagorean triple
Note two curiosities for 6th term p(6) = cat(461, 280, 261) = prime(24423734):
cat(261, 380, 461): 261380461 = prime(14267135) also prime, SMALLEST of this type
Additionally p(6) is also the FIRST such concatenation with a prime hypotenuse: 461 = prime(89) Same is true for p(8) = 1249960799 = prime(62841771), 7999601249 = prime(367766086), 1249 = prime(204)
p(15) = 25812460781 = prime(1125896092), 78124602581 = prime(3250321954)
but hypotenuse 2581 = 29 * 89 and short leg 781 = 11 * 71 are both composite
p(18) = 47094700291= prime(2001581081), 29147004709 = prime(1264629019), 4709 = 17 * 277, 291 = 3 * 97
REFERENCES
W. W. R. Ball, H. S. M. Coxeter: Mathematical Recreations and Essays, New York: Dover, 1987
L. E. Dickson: "Rational Right Triangles", ch. 4 in History of the Theory of numbers, vol. II, Dover Publications 2005
W. Sierpinski: Pythagorean Triangles, Mineola, NY, Dover Publications, Inc, 2003
EXAMPLE
25^2 = 24^2 + 7^2, and cat(25, 24, 7) = 25247 is prime, so 25247 is in the sequence.
5^2 = 4^2 + 3^2, but cat(5, 4, 3) = 543 = 3*181 is not prime, so 543 is not in the sequence.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 30 2010
EXTENSIONS
Edited by Franklin T. Adams-Watters, Aug 27 2012
STATUS
approved