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A082542
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a(n) = prime(n) + 2 - (prime(n) mod 4).
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4
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2, 2, 6, 6, 10, 14, 18, 18, 22, 30, 30, 38, 42, 42, 46, 54, 58, 62, 66, 70, 74, 78, 82, 90, 98, 102, 102, 106, 110, 114, 126, 130, 138, 138, 150, 150, 158, 162, 166, 174, 178, 182, 190, 194, 198, 198, 210, 222, 226, 230, 234, 238, 242, 250, 258, 262, 270, 270, 278
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OFFSET
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1,1
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COMMENTS
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For k > 1: a(k+1) = a(k) if and only if prime(k) == 1 modulo 4 and prime(k+1) = prime(k) + 2, see A071695 and A071696.
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LINKS
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FORMULA
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a(n+1) = p + (-1/p) = p + (-1)^{(p-1)/2)}, where p is the n-th odd prime and (a/b) denotes the value of Legendre symbol. - Lekraj Beedassy, Mar 17 2005
Product_{n>=1} a(n)/prime(n) = 2/Pi (A060294). (End)
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EXAMPLE
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a(2) = 2 because the second prime is 3, and 3 + 2 - 3 = 2.
a(3) = 6 because the third prime is 5, and 5 + 2 - 1 = 6.
a(4) = 6 because the fourth prime is 7, and 7 + 2 - 3 = 6.
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MATHEMATICA
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Table[Prime[n] + 2 - Mod[Prime[n], 4], {n, 60}] (* Alonso del Arte, Feb 23 2015 *)
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PROG
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(PARI) vector(60, n, 2 + prime(n) - lift(Mod(prime(n), 4))) \\ G. C. Greubel, Nov 14 2018
(Magma) [2 + NthPrime(n) - (NthPrime(n) mod 4): n in [1..60]]; // G. C. Greubel, Nov 14 2018
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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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