A105318 Starting prime for the smallest prime Pythagorean sequence for n triangles.

5, 3, 271, 169219, 356498179, 2500282512131, 20594058719087111, 2185103796349763249

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..8.

H. Dubner, Posting to Number Theory List

T. Forbes, Posting to Number Theory List

H. Dubner & T. Forbes, Prime Pythagorean Triangles

T. Forbes, Posting to Number Theory List

H. Dubner & T. Forbes, Journal of Integer Sequences, Vol. 4(2001) #01.2.3, Prime Pythagorean triangles

C. K. Caldwell, The Prime Glossary, Pythagorean triples

Example

5 is a(1) because (5^2+1)/2 = 13 is prime, but (13^2+1)/2 = 85 is not.

Crossrefs

Cf. A048161, A048270, A048295, A308635, A308636.

Sequence in context: A264738 A002208 A100653 * A304287 A121021 A237518

Adjacent sequences: A105315 A105316 A105317 * A105319 A105320 A105321

Keyword

hard,more,nonn

Author

Lekraj Beedassy, Apr 26 2005

Extensions

a(1) added by T. D. Noe, Jan 29 2011

Status

approved