cp's OEIS Frontend

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

%I A174825 #4 Aug 27 2012 02:28:43
%S A174825 25247,18517657,42541687,48148031,305224207,461380261,929920129,
%T A174825 1249960799,4141414091,13811020931,17451736177,18011680649,
%U A174825 19011820549,22852204603,25812460781,27492580949,39653956267,47094700291
%N A174825 Prime concatenations p = concatenation of c, b, and a where a, b, c is a primitive Pythagorean triple, a < b < c.
%C A174825 c^2 = b^2 + a^2 with c > b > a relatively prime, i.e. a primitive Pythagorean triple
%C A174825 Note two curiosities for 6th term p(6) = cat(461, 280, 261) = prime(24423734):
%C A174825 cat(261, 380, 461): 261380461 = prime(14267135) also prime, SMALLEST of this type
%C A174825 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)
%C A174825 p(15) = 25812460781 = prime(1125896092), 78124602581 = prime(3250321954)
%C A174825 but hypotenuse 2581 = 29 * 89 and short leg 781 = 11 * 71 are both composite
%C A174825 p(18) = 47094700291= prime(2001581081), 29147004709 = prime(1264629019), 4709 = 17 * 277, 291 = 3 * 97
%D A174825 W. W. R. Ball, H. S. M. Coxeter: Mathematical Recreations and Essays, New York: Dover, 1987
%D A174825 L. E. Dickson: "Rational Right Triangles", ch. 4 in History of the Theory of numbers, vol. II, Dover Publications 2005
%D A174825 W. Sierpinski: Pythagorean Triangles, Mineola, NY, Dover Publications, Inc, 2003
%e A174825 25^2 = 24^2 + 7^2, and cat(25, 24, 7) = 25247 is prime, so 25247 is in the sequence.
%e A174825 5^2 = 4^2 + 3^2, but cat(5, 4, 3) = 543 = 3*181 is not prime, so 543 is not in the sequence.
%Y A174825 Cf. A020882, A008846
%K A174825 base,nonn
%O A174825 1,1
%A A174825 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 30 2010
%E A174825 Edited by _Franklin T. Adams-Watters_, Aug 27 2012