A048851 Length of hypotenuse squared in right triangle formed by a prime spiral plotted in Cartesian coordinates.

8, 13, 34, 74, 170, 290, 458, 650, 890, 1370, 1802, 2330, 3050, 3530, 4058, 5018, 6290, 7202, 8210, 9530, 10370, 11570, 13130, 14810, 17330, 19610, 20810, 22058, 23330, 24650, 28898, 33290, 35930, 38090, 41522, 45002, 47450, 51218, 54458

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

Table of n, a(n) for n=1..39.

Formula

To begin prime spiral, plot (2, 0), (0, 2). Square of hypotenuse is c^2 = a^2 + b^2, or 8 = 4 + 4, so a(1) = 8.

a(n) = A069484(n-1), n >= 2. - Mamuka Jibladze, Mar 24 2017

Example

a(2) = 13 because c^2 = a^2 + b^2 = 4 + 9 = 13.

Crossrefs

Cf. A006094.

Sequence in context: A354595 A063585 A258768 * A039298 A360790 A218627

Adjacent sequences: A048848 A048849 A048850 * A048852 A048853 A048854

Keyword

easy,nonn

Author

Enoch Haga

Status

approved