A159464 Indices of "Pithagorean" (not Pythagorean!) triples with prime initial terms.

1701, 51912, 377402, 388105, 1598877, 46208786, 212204419, 51398524, 91140956, 145796362, 133289691, 109954, 344895386

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..13.

Xavier Gourdon, Pifast43

Cino Hilliard, Pithagorean triples

Formula

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.

Example

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...

Prog

(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.

Crossrefs

Sequence in context: A020405 A091368 A263344 * A166400 A210121 A345506

Adjacent sequences: A159461 A159462 A159463 * A159465 A159466 A159467

Keyword

base,more,nonn

Author

Cino Hilliard, Apr 13 2009

Status

approved