A181055 Numbers n such that sum_{k=1..n} (-1)^(n-k) *bigomega(k) is prime.

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

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)^ (6-k)*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)^(n-k))*bigomega(k):od: if type(s, prime)=true then printf(`%d, `, n):else fi:od:

Crossrefs

Cf. A001222.

Sequence in context: A053012 A359202 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