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A105318 Starting prime for the smallest prime Pythagorean sequence for n triangles. 4
5, 3, 271, 169219, 356498179, 2500282512131, 20594058719087111, 2185103796349763249 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 11:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)