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

1,1

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.

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.

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 *)

Prog

(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

Crossrefs

Cf. A069485, A075892, A069482, A069486.

Cf. A001248, A000040, A048851.

Sequence in context: A190458 A180673 A081752 * A089113 A067430 A214729

Adjacent sequences: A069481 A069482 A069483 * A069485 A069486 A069487

Keyword

nonn,easy

Author

Reinhard Zumkeller, Mar 29 2002

Status

approved