A342567 - OEIS

%I #19 Jul 15 2024 16:08:17

%S 2,-3,15,-9,21,-15,-11,64,-56,49,45,-39,-35,18,124,-116,79,75,-140,91,

%T -71,-65,210,105,-99,111,-105,-537,663,-119,280,-546,606,-296,18,175,

%U -155,18,364,-714,774,-189,201,-983,72,916,231,-225,-221,484,-954,532,18,18

%N a(n) = (prime(n)^2 - prime(n-1)*prime(n+1))/2, n >= 3.

%H Hugo Pfoertner, <a href="/A342567/b342567.txt">Table of n, a(n) for n = 3..10000</a>

%F a(n) = A056221(n-1)/2 for n >= 3.

%t a[n_]:=(Prime[n]^2 - Prime[n-1]*Prime[n+1])/2; Array[a,54,3] (* _Stefano Spezia_, Jul 15 2024 *)

%o (PARI) forprime(p=5,265,my(pp=precprime(p-1),pn=nextprime(p+1));print1((p^2-pp*pn)/2,", "))

%o (Python)

%o from primesieve.numpy import n_primes

%o primesarray = numpy.array(n_primes(10005,1))

%o for i in range (2, 10003):

%o      print(((primesarray[i]**2)-(primesarray[i-1]*primesarray[i+1]))//2)

%o      # _Karl-Heinz Hofmann_, Jun 20 2021

%Y Cf. A056221.

%K sign,easy

%O 3,1

%A _Hugo Pfoertner_, Jun 20 2021