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A186201 Consider all ways of writing 2n = p + q where p, q are primes, p <= n and q >= n; let s1(n) = sum of the p's and s2(n) = sum of the q's; the sequence lists the integers 2n for which s1(n) divides s2(n). 2
4, 6, 16, 18, 20, 32, 52, 72, 102, 180, 3212 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Comment from N. J. A. Sloane, Mar 10 2011: This is a list of values of 2n such that A185297(n) divides A187129(n).

Comment from T. D. Noe, Mar 10 2011: I have some fast code for counting Goldbach partitions.  I made a slight change so that it sums the partitions instead.  Using this new program, I did not find any additional terms < 10^7.

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

For 2n=52, the partitions are (5,47), (11,41) and (23,29).  The lesser sum of primes is 5+11+23=39 and the greater sum of primes is 29+41+47=117, with 39|117 for quotient 3.

For the 2n listed, the values of (s1(n), s2(n)/s1(n)) are (2,1), (3,1), (8,3), (12,2), (10,3), (16,3), (39,3), (108,3), (204,3), (630,3), (35332,3).

MATHEMATICA

okQ[n_] := Module[{p, q}, p = Select[Prime[Range[PrimePi[n]]], PrimeQ[2 n - #] &]; q = 2 n - p; Mod[Plus @@ q, Plus @@ p] == 0]; 2*Select[Range[2, 10000], okQ]

CROSSREFS

Cf. A045917, A185297, A187129.

Sequence in context: A240034 A302122 A056222 * A138624 A071428 A117988

Adjacent sequences:  A186198 A186199 A186200 * A186202 A186203 A186204

KEYWORD

nonn,more

AUTHOR

J. M. Bergot, Feb 14 2011

STATUS

approved

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Last modified October 22 05:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)