A181057 Numbers n such that Sum_{k=1..n} (-1)^(n-k) *phi(2*k) is prime.

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

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)^(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:

Mathematica

Select[Range[150], PrimeQ[Sum[(-1)^(#-k) EulerPhi[2k], {k, #}]]&] (* Harvey P. Dale, Jul 16 2024 *)

Crossrefs

Cf. A000010, A062570.

Sequence in context: A079000 A357122 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