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A342567 a(n) = (prime(n)^2 - prime(n-1)*prime(n+1))/2, n >= 3.

%I A342567 #19 Jul 15 2024 16:08:17
%S A342567 2,-3,15,-9,21,-15,-11,64,-56,49,45,-39,-35,18,124,-116,79,75,-140,91,
%T A342567 -71,-65,210,105,-99,111,-105,-537,663,-119,280,-546,606,-296,18,175,
%U A342567 -155,18,364,-714,774,-189,201,-983,72,916,231,-225,-221,484,-954,532,18,18
%N A342567 a(n) = (prime(n)^2 - prime(n-1)*prime(n+1))/2, n >= 3.
%H A342567 Hugo Pfoertner, <a href="/A342567/b342567.txt">Table of n, a(n) for n = 3..10000</a>
%F A342567 a(n) = A056221(n-1)/2 for n >= 3.
%t A342567 a[n_]:=(Prime[n]^2 - Prime[n-1]*Prime[n+1])/2; Array[a,54,3] (* _Stefano Spezia_, Jul 15 2024 *)
%o A342567 (PARI) forprime(p=5,265,my(pp=precprime(p-1),pn=nextprime(p+1));print1((p^2-pp*pn)/2,", "))
%o A342567 (Python)
%o A342567 from primesieve.numpy import n_primes
%o A342567 primesarray = numpy.array(n_primes(10005,1))
%o A342567 for i in range (2, 10003):
%o A342567      print(((primesarray[i]**2)-(primesarray[i-1]*primesarray[i+1]))//2)
%o A342567      # _Karl-Heinz Hofmann_, Jun 20 2021
%Y A342567 Cf. A056221.
%K A342567 sign,easy
%O A342567 3,1
%A A342567 _Hugo Pfoertner_, Jun 20 2021