|
%I #17 Apr 03 2023 10:36:10
%S 5,3,271,169219,356498179,2500282512131,20594058719087111,
%T 2185103796349763249
%N Starting prime for the smallest prime Pythagorean sequence for n triangles.
%C Smallest prime p(0) such that the n-chain governed by recurrence p(i+1)=(p(i)^2 + 1)/2 are all primes. Equivalently, least prime p(0) that generates a sequence of n 2-prime triangles, where p(k) is the hypotenuse of the k-th triangle and the leg of the (k+1)-th triangle.
%H H. Dubner, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;905120b.9907">Posting to Number Theory List</a>
%H T. Forbes, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;12f3035e.9907">Posting to Number Theory List</a>
%H H. Dubner & T. Forbes, <a href="https://t5k.org/references/docs/pyth0704.pdf">Prime Pythagorean Triangles</a>
%H T. Forbes, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;c670c8fd.9910">Posting to Number Theory List</a>
%H H. Dubner & T. Forbes, Journal of Integer Sequences, Vol. 4(2001) #01.2.3, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/DUBNER/pyth.html">Prime Pythagorean triangles</a>
%H C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php/PrmPythagTriples.html">Pythagorean triples</a>
%e 5 is a(1) because (5^2+1)/2 = 13 is prime, but (13^2+1)/2 = 85 is not.
%Y Cf. A048161, A048270, A048295, A308635, A308636.
%K hard,more,nonn
%O 1,1
%A _Lekraj Beedassy_, Apr 26 2005
%E a(1) added by _T. D. Noe_, Jan 29 2011
| 