A245646 The smallest member 'a' of the Pythagorean triples (a,b,c) ordered by increasing c, where the triples consist of a triangular number, a square number and a pentagonal number.

3, 9, 100, 900

Offset: 1

Author

Ivan N. Ianakiev, Jul 28 2014

Keywords

• nonn
• more
• hard

Comments

The next term (if it exists) comes from a triple with c > 10^5.

Examples

			a(1) = 3 as the first such Pythagorean triple is (3,4,5). The next three triples are (9,12,15), (100,105,145), (900,2625,2775).
		

Crossrefs

Cf. A000217, A000290, A000326, A245647, A245648

Programs

Mathematica

n=10^3;ppt={};list={};pos=1;t[x_]:=(IntegerPart[Sqrt[2*x]])*(IntegerPart[Sqrt[2*x]]+1)/2;ls[x_]:=Length[Sqrt[x]];lis[x_]:=Length[IntegerPart[Sqrt[x]]];lp[x_]:=Length[(Sqrt[24*x+1]+1)/6];lip[x_]:=Length[IntegerPart[(Sqrt[24*x+1]+1)/6]];Do[y=x+1;z=y+1;While[z<=n,While[z^2