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A330560
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a(n) = number of primes p <= prime(n) with Delta(p) == 2 (mod 4), where Delta(p) = nextprime(p) - p.
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3
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0, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 10, 11, 12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18, 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 29, 30, 30, 30, 30, 31, 31, 32, 33, 34, 35, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43, 43, 44, 45, 46, 47, 47, 48, 48, 49, 50, 50, 51, 51, 51, 51, 52, 53, 54
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OFFSET
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1,3
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LINKS
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MAPLE
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N:= 200: # for a(1)..a(N)
P:= [seq(ithprime(i), i=1..N+1)]:
Delta:= P[2..-1]-P[1..-2] mod 4:
R:= map(charfcn[2], Delta):
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MATHEMATICA
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Accumulate[Map[Boole[Mod[#, 4] == 2]&, Differences[Prime[Range[100]]]]] (* Paolo Xausa, Feb 05 2024 *)
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PROG
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(Magma) [#[p:p in PrimesInInterval(1, NthPrime(n))| (NextPrime(p)-p) mod 4 eq 2]:n in [1..90]]; // Marius A. Burtea, Dec 31 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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