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a(n) = prime(n+1)^2 + prime(n)^2.
23

%I #34 Feb 16 2022 01:56:51

%S 13,34,74,170,290,458,650,890,1370,1802,2330,3050,3530,4058,5018,6290,

%T 7202,8210,9530,10370,11570,13130,14810,17330,19610,20810,22058,23330,

%U 24650,28898,33290,35930,38090,41522,45002

%N a(n) = prime(n+1)^2 + prime(n)^2.

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

%H Charles R Greathouse IV, <a href="/A069484/b069484.txt">Table of n, a(n) for n = 1..10000</a>

%H Janyarak Tongsomporn, Saeree Wananiyaku, and Jörn Steuding, <a href="http://math.colgate.edu/~integers/w9/w9.pdf">Sums of consecutive prime squares</a>, Integers (2022) Vol. 22, #A9.

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

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

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

%p seq(ithprime(n)^2+ithprime(n+1)^2, n = 1 .. 100); # _Stefano Spezia_, Dec 21 2018

%t Table[Prime[n]^2+Prime[n+1]^2,{n,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 12 2010 *)

%t Total[#^2]&/@Partition[Prime[Range[50]],2,1] (* _Harvey P. Dale_, May 26 2012 *)

%o (PARI) v=primes(101);vector(#v-1,i,v[i]^2+v[i+1]^2) \\ _Charles R Greathouse IV_, Aug 21 2011

%o (Python)

%o from sympy import prime

%o for n in range(1,101): print(n, prime(n)**2+prime(n+1)**2) # _Stefano Spezia_, Dec 21 2018

%Y Cf. A069485, A075892, A069482, A069486.

%Y Cf. A001248, A000040, A048851.

%K nonn,easy

%O 1,1

%A _Reinhard Zumkeller_, Mar 29 2002