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A330561 a(n) = number of primes p <= prime(n) with Delta(p) == 0 (mod 4), where Delta(p) = nextprime(p) - p.

%I A330561 #29 Feb 06 2024 08:13:19
%S A330561 0,0,0,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,7,7,8,9,9,10,10,11,11,12,
%T A330561 12,12,12,12,12,12,13,13,13,13,13,13,14,14,15,16,17,17,18,18,18,18,18,
%U A330561 18,18,18,18,19,19,19,19,20,20,21,21,21,21,21,22,22,23,23,23,24,24,25,26,27,27,27,27,27
%N A330561 a(n) = number of primes p <= prime(n) with Delta(p) == 0 (mod 4), where Delta(p) = nextprime(p) - p.
%H A330561 Robert Israel, <a href="/A330561/b330561.txt">Table of n, a(n) for n = 1..10000</a>
%p A330561 N:= 200: # for a(1)..a(N)
%p A330561 P:= [seq(ithprime(i),i=1..N+1)]:
%p A330561 Delta:= P[2..-1]-P[1..-2] mod 4:
%p A330561 R:= map(charfcn[0],Delta):
%p A330561 ListTools:-PartialSums(R); # _Robert Israel_, Dec 31 2019
%t A330561 Accumulate[Map[Boole[Mod[#, 4] == 0]&, Differences[Prime[Range[100]]]]] (* _Paolo Xausa_, Feb 05 2024 *)
%o A330561 (Magma) [#[p:p in PrimesInInterval(1,NthPrime(n))|IsIntegral((NextPrime(p)-p)/4)]:n in [1..80]]; // _Marius A. Burtea_, Dec 31 2019
%Y A330561 Cf. A098059.
%Y A330561 Sequences related to the differences between successive primes: A001223 (Delta(p)), A028334, A080378, A104120, A330556, A330557, A330558, A330559, A330560.
%K A330561 nonn
%O A330561 1,6
%A A330561 _N. J. A. Sloane_, Dec 30 2019