

A181055


Numbers n such that sum_{k=1..n} (1)^(nk) *bigomega(k) is prime.


0



4, 6, 8, 10, 12, 24, 26, 28, 30, 32, 34, 46, 52, 70, 78, 82, 102, 126, 128, 132, 134, 136, 138, 168, 186, 190, 192, 222, 234, 274, 280, 312, 316, 322, 336, 378, 418, 424, 426, 440, 472, 484, 492, 504, 532, 540, 558, 570, 574, 584, 592, 602, 604, 606, 650, 652
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OFFSET

1,1


COMMENTS

The partial alternating sum over bigomega(.)=A001222(.) in the definition starts at n=1
as 0, 1, 0, 2, 1, 3, 2, 5, 3, 5, 4, 7, 6, 8 ...
The first primes in this signed sequence are
2, 3, 5, 5, 7, 17, 17, 17, 19, 23, 23, 31, 37, 53, 59, 61, 79, 97, 103, 107, 107, 107, 109,...
occurring at positions 4, 6, 8, 10 etc, which define the sequence.


LINKS

Table of n, a(n) for n=1..56.


EXAMPLE

6 is in the sequence because sum_{k=1..6}(1)^ (6k)*bigomega(k) =
((1)^5)*0 + ((1)^4)*1 + ((1)^3)*1 + ((1)^2)*2 + ((1)^1)*1 + ((1)^0)*2 =
0 + 1 1 + 2 1 + 2 = 3 is prime.


MAPLE

with(numtheory):for n from 1 to 1000 do: s:=0: for k from 1 to n do :s:=s+((1)^(nk))*bigomega(k):od: if type(s, prime)=true then printf(`%d, `, n):else fi:od:


CROSSREFS

Cf. A001222.
Sequence in context: A131694 A053012 A096160 * A225506 A073669 A073670
Adjacent sequences: A181052 A181053 A181054 * A181056 A181057 A181058


KEYWORD

nonn


AUTHOR

Michel Lagneau, Oct 01 2010


EXTENSIONS

Comment slightly extended  R. J. Mathar, Oct 03 2010


STATUS

approved



