A069484 a(n) = prime(n+1)^2 + prime(n)^2.

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

Offset: 1

Author

Reinhard Zumkeller, Mar 29 2002

Keywords

• nonn
• easy

Comments

Together with A069482(n) and A069486(n) a Pythagorean triangle is formed with area = A069487(n).

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Janyarak Tongsomporn, Saeree Wananiyaku, and Jörn Steuding, Sums of consecutive prime squares, Integers (2022) Vol. 22, #A9.

Crossrefs

Cf. A069485, A075892, A069482, A069486.

Cf. A001248, A000040, A048851.

Programs

Maple

seq(ithprime(n)^2+ithprime(n+1)^2, n = 1 .. 100); # Stefano Spezia, Dec 21 2018

Mathematica

Table[Prime[n]^2+Prime[n+1]^2,{n,5!}] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2010 *)
Total[#^2]&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, May 26 2012 *)

PARI

v=primes(101);vector(#v-1,i,v[i]^2+v[i+1]^2) \\ Charles R Greathouse IV, Aug 21 2011

Python

from sympy import prime
for n in range(1,101): print(n, prime(n)**2+prime(n+1)**2) # Stefano Spezia, Dec 21 2018

Formula

a(n) = A001248(n+1) + A001248(n) = A000040(n+1)^2 + A000040(n)^2.

a(n) = A048851(n+1).

a(n) = 2 * A075892(n) for n > 1.