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 A181057 Numbers n such that Sum_{k=1..n} (-1)^(n-k) *phi(2*k) is prime. 0
 4, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 23, 25, 26, 27, 28, 30, 31, 33, 35, 39, 40, 41, 42, 43, 44, 45, 46, 48, 51, 52, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 71, 72, 74, 75, 77, 78, 79, 80, 81, 88, 89, 90, 91, 94, 95, 96, 97, 98, 99, 100, 102, 103, 105, 108, 109 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The partial alternating sum over phi(.) = A000010(.) in the definition starts at n = 1 as 1, 1, 1, 3, 1, 3, 3, 5, 1, 7, 3, 5, 7, 5, 3, 13, ... The first primes in this auxiliary sequence are 3, 3, 3, 5, 7, 3, 5, 7, 5, 3, 13, 3, 7, 5, 7, 11, 13, 5, 19, 7, 23, 11, 3, 3, 29, 11, 13, ... occurring at positions 4, 6, 7, 8, etc., which define the sequence. LINKS EXAMPLE 4 is in the sequence because Sum_{k=1..4} (-1)^(4-k)*phi(2*k) = ((-1)^3)*1 + ((-1)^2)*2 + ((-1)^1)*2 + ((-1)^0)*4 = -1 + 2 - 2 + 4 = 3 is prime. MAPLE with(numtheory):for n from 1 to 200 do:x:=sum((((-1)^(n-k))*phi(2*k), k=1..n)): if type(x, prime)=true then printf(`%d, `, n):else fi:od: CROSSREFS Cf. A000010, A062570. Sequence in context: A299411 A079000 A047509 * A151757 A171413 A225551 Adjacent sequences:  A181054 A181055 A181056 * A181058 A181059 A181060 KEYWORD nonn AUTHOR Michel Lagneau, Oct 01 2010 EXTENSIONS Comment slightly extended by R. J. Mathar, Oct 03 2010 STATUS approved

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Last modified December 4 13:06 EST 2021. Contains 349526 sequences. (Running on oeis4.)