A077020 a(n) is the unique odd positive solution x of 2^n = 7x^2+y^2.

1, 1, 1, 3, 1, 5, 7, 3, 17, 11, 23, 45, 1, 91, 89, 93, 271, 85, 457, 627, 287, 1541, 967, 2115, 4049, 181, 8279, 7917, 8641, 24475, 7193, 41757, 56143, 27371, 139657, 84915, 194399, 364229, 24569, 753027, 703889, 802165, 2209943, 605613

Offset: 3

Author

Ed Pegg Jr, Oct 17 2002

Keywords

• nonn

Comments

The sequences A001607, A077020, A107920, A167433, A169998 are all essentially the same except for signs.

Examples

			G.f. = x^3 + x^4 + x^5 + 3*x^6 + x^7 + 5*x^8 + 7*x^9 + 3*x^10 + 17*x^11 + ...
a(3)=1 since 2^3=8=7*1^2+1^2, a(6)=3 since 2^6=64=7*3^2+1^2.
		

References

• A. Engel, Problem-Solving Strategies. p. 126.

Links

• T. D. Noe, Table of n, a(n) for n=3..500
• Eric Weisstein's World of Mathematics, Diophantine Equations 2nd Powers

Crossrefs

a(n)=abs(A001607(n-2)).

Cf. A077021.

Formula

a(n) = 2^(n-2) * a(4-n) for all n in Z. - Michael Somos, Jan 05 2017

0 = 8*a(n)^2 + 2*a(n+1)^2 - a(n+2)^2 - a(n+3)^2 for all n in Z. - Michael Somos, Jan 05 2017

2*a(n) + a(n+1) = a(n+2) or a(n+3). - Michael Somos, Jan 05 2017