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

1,1

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A002113.

An analog of the prime spiral of A048851.

Sequence in context: A178621 A362105 A309230 * A324702 A072921 A369714

Adjacent sequences: A048868 A048869 A048870 * A048872 A048873 A048874

Keyword

easy,nonn,base,nice

Author

Enoch Haga

Status

approved