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A216052 The sum of the primes less than or equal to n minus the sum of the distinct elements of the Goldbach partitions of n. 1
0, 2, 5, 3, 5, 7, 10, 9, 8, 2, 28, 16, 28, 20, 26, 9, 58, 22, 58, 37, 56, 22, 100, 28, 75, 35, 100, 44, 129, 39, 129, 96, 127, 41, 160, 16, 197, 140, 158, 77, 238, 70, 238, 149, 236, 120, 328, 88, 279, 128, 328, 172, 381, 111, 326, 213, 381, 178, 440, 80, 440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If n is prime then a(n) sets or equals a record.

If n and n+2 are twin primes then a(n) = a(n+2).

LINKS

J. Stauduhar, Table of n, a(n) for n = 1..10000

EXAMPLE

With n = 2, the sum of the primes <= 2 is 2, and the sum of the distinct elements of the Goldbach partitions of 2 is 0, so a(2) = 2 + 0 = 2.

With n = 4, the sum of the primes <= 4 is 5, and the sum of the distinct elements of the Goldbach partitions of is 2, so a(4) = 5 - 2 = 3.

MATHEMATICA

f[n_] := Module[{lst={}}, For[i=1, i<=n, i++, t = Plus @@ Select[ Table[Prime[i], {i, PrimePi[i]}], !PrimeQ[i-#]&]; AppendTo[lst, t]]; lst]; f[1000] (* J. Stauduhar, Sep 22 2012 *)

CROSSREFS

Sequence in context: A249273 A078376 A226123 * A021911 A248852 A299210

Adjacent sequences:  A216049 A216050 A216051 * A216053 A216054 A216055

KEYWORD

nonn

AUTHOR

J. Stauduhar, Sep 22 2012

STATUS

approved

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Last modified May 10 05:05 EDT 2021. Contains 343748 sequences. (Running on oeis4.)