A159464 - OEIS

%I #14 Aug 18 2018 08:32:15

%S 1701,51912,377402,388105,1598877,46208786,212204419,51398524,

%T 91140956,145796362,133289691,109954,344895386

%N Indices of "Pithagorean" (not Pythagorean!) triples with prime initial terms.

%C In theory, it would seem this sequence is infinite even though only triples up prime 43 are found in the first 1 billion digits of Pi. The odds of finding a hit can be overwhelming as the number of digits in the triples becomes large. My guess is this observable universe is finite.

%H Xavier Gourdon, <a href="http://numbers.computation.free.fr/Constants/PiProgram/pifast.html">Pifast43</a>

%H Cino Hilliard, <a href="http://groups.google.com/group/gmpforfun/web/pithagorean">Pithagorean triples</a>

%F A "Pithagorean" triple is a Pythagorean triple whose concatenated digits are found in the digital expansion of Pi. This sequence is a special case of the index when the first term of the triple is and odd prime.

%e The concatenated Pythagorean triple 345 is found starting in position 1701 of the expansion of the digits of Pi. Reading a Pifast43 compressed file enables you to search huge strings. The Gcc program adjusts for the first 2 lines of output by pifast43. Pi with 10000 digits: Pi = 3. 1701 141592653589793238...33239073941433345...

%o (Other) Use the Gcc program in the link to read a Pi digits file created by pifast43 also in a link. The process is described in the Gcc link.

%K base,more,nonn

%O 1,1

%A _Cino Hilliard_, Apr 13 2009