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A308754
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a(0) = 0, a(n) = a(n-1) + 1 if 2*n + 3 is prime, otherwise a(n) = a(n-1).
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1
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0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 7, 8, 9, 9, 9, 10, 10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 16, 16, 16, 17, 17, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 28, 28, 28, 28, 28, 28, 29, 29, 30, 30, 30, 31
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = a(n-1) + A101264(n+1), n > 0.
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EXAMPLE
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a(0) = 0 (by definition).
a(1) = 1 = a(0) + 1, because 2*1 + 3 is prime;
a(2) = 2 = a(1) + 1, because 2*2 + 3 is prime;
a(3) = 2 = a(2), because 2*3 + 3 is not prime;
a(4) = 3 = a(3) + 1, because 2*4 + 3 is prime.
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MATHEMATICA
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a[0] = 0; a[n_] := a[n] = a[n - 1] + Boole@PrimeQ[2 n + 3]; Array[a, 100, 0] (* Amiram Eldar, Jul 06 2019 *)
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PROG
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(BASIC)
' p(n) contains the prime sequence except for 2. p(0)=3
' output in the a(n) sequence for 0 <= n <= maxterm
ip = -1
For n = 0 To maxterm
If (2 * n + 3) = p(ip+1) Then
ip = ip + 1
End If
a(n) = ip
Next n
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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