A174825 Prime concatenations p = concatenation of c, b, and a where a, b, c is a primitive Pythagorean triple, a < b < c.

25247, 18517657, 42541687, 48148031, 305224207, 461380261, 929920129, 1249960799, 4141414091, 13811020931, 17451736177, 18011680649, 19011820549, 22852204603, 25812460781, 27492580949, 39653956267, 47094700291

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

Links

Table of n, a(n) for n=1..18.

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

Cf. A020882, A008846

Sequence in context: A226501 A046709 A179723 * A269041 A130615 A175741

Adjacent sequences: A174822 A174823 A174824 * A174826 A174827 A174828

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