A048871 Length of hypotenuse squared in right triangle formed by a palindromic spiral plotted in Cartesian coordinates.

2, 5, 13, 25, 41, 61, 85, 113, 145, 202, 605, 1573, 3025, 4961, 7381, 10285, 13673, 17545, 20002, 22522, 26962, 31802, 37042, 42682, 48722, 55162, 62002, 69242, 77285, 85748, 94228, 103108, 112388, 122068, 132148, 142628, 153508, 164788

Offset: 1

Author

Enoch Haga

Keywords

• easy
• nonn
• base
• nice

Examples

			To begin palindromic spiral, plot (1, 0), (0, 1). Hypotenuse is c^2=a^2+b^2, or 2=1+1. a(1) = 2.
a(2)=5 because c^2=a^2+b^2 and 5=1+4.
		

References

• H. E. Huntley, The Divine Proportion, A Study in Mathematical Beauty. New York: Dover, 1970. See Chapter 13, Spira Mirabilis, especially Fig. 13-5, page 173.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Patrick De Geest, World!Of Numbers

Crossrefs

Cf. A002113.

An analog of the prime spiral of A048851.

Programs

Mathematica

Join[{2},Total[#^2]&/@Partition[Select[Range[300],PalindromeQ],2,1]] (* Harvey P. Dale, Mar 18 2024 *)

Formula

a(n) = A002113(n)^2 + A002113(n-1)^2, n > 1.