A303734 a(n) = ((2n+1)^(2n^2+2n)+(2n^2+2n)^(2n+1))/(2n^2+2n+1).

29, 18799189, 7663249255406115433, 3605093400349900568684962740253251161, 4991502287564231140564742546889815977689154940104978501999141, 43835167264777185998985243579910029928546583864541049798936281152692136028486139208681333389

Offset

1,1

Comments

If (a, b, c) is a primitive Pythagorean triple such that a^2+b^2 = c^2, where b is the even leg and b = c-1 then a^b + b^a is divisible by c. See Joardar link. To generate the n-th such Pythagorean triple we take a = 2n+1, b = 2n^2+2n and c = 2n^2+2n+1. This sequence is the quotient (a^b+b^a)/c, i.e., a(n) = ((2n+1)^(2n^2+2n)+(2n^2+2n)^(2n+1))/(2n^2+2n+1).

Links

Table of n, a(n) for n=1..6.

B. Joardar, A Property of Primitive Pythagorean Triples, At Right Angles, August 2017, Azim Premji University, India.

Wikipedia, Almost-isosceles Pythagorean triples.

Example

a(2) = 18799189 because n = 2 generates the primitive Pythagorean triple (5, 12, 13) and (5^12+12^5)/13 = 18799189.

Mathematica

a[n_] := ((2n+1)^(2n^2+2n)+(2n^2+2n)^(2n+1))/(2n^2+2n+1); Array[a, 6]

Crossrefs

Cf. A001844.

Sequence in context: A185822 A321666 A139775 * A087528 A307622 A219015

Adjacent sequences: A303731 A303732 A303733 * A303735 A303736 A303737

Keyword

nonn

Author

Frank M Jackson, Apr 29 2018

Status

approved