

A181057


Numbers n such that Sum_{k=1..n} (1)^(nk) *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
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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

Table of n, a(n) for n=1..69.


EXAMPLE

4 is in the sequence because Sum_{k=1..4} (1)^(4k)*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)^(nk))*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



