A082918 -id:A082918 - cp's OEIS frontend

A082917 Numbers that can be expressed as the sum of two odd primes in more ways than any smaller even number.

6, 10, 22, 34, 48, 60, 78, 84, 90, 114, 120, 168, 180, 210, 300, 330, 390, 420, 510, 630, 780, 840, 990, 1050, 1140, 1260, 1470, 1650, 1680, 1890, 2100, 2310, 2730, 3150, 3570, 3990, 4200, 4410, 4620, 5250, 5460, 6090, 6510, 6930, 7980, 8190, 9030, 9240

Offset: 1

Hugo Pfoertner, Apr 15 2003

nonn

The terms up to 114 are identical with A001172. The record-setting number of decompositions is given by A082918.

It appears that every primorial number (A002110) greater than 30 is in this sequence. Sequence A116979 gives the number of decompositions for n equal to a primorial number. - T. D. Noe, Mar 15 2010

			a(1) = 6 = 3 + 3.
a(2) = 10 because 10 is the smallest number that can be written in two ways: 10 = 3 + 7 = 5 + 5.

Bill Hannaford, Table of n, a(n) for n = 1..420 (first 244 terms from T. D. Noe)

Cf. A002375, A001172, A082918. A109679 is another version of the same sequence.

kmax = 40000;
ip[k_] := IntegerPartitions[k, {2}, Select[Range[3, k-1], PrimeQ]];
seq = Module[{k, lg, record = 0, n = 0}, Reap[For[k = 6, k <= kmax, k = k+2, lg = Length[ip[k]]; If[lg > record, record = lg; n = n+1; Print["a(", n, ") = ", k]; Sow[k]]]][[2, 1]]] (* Jean-François Alcover, Jun 04 2022 *)

A109679 Smallest even number which is the unordered sum of two primes in more ways than any previous even number.

Original entry on oeis.org

2, 4, 10, 22, 34, 48, 60, 78, 84, 90, 114, 120, 168, 180, 210, 300, 330, 390, 420, 510, 630, 780, 840, 990, 1050, 1140, 1260, 1470, 1650, 1680, 1890, 2100, 2310, 2730, 3150, 3570, 3990, 4200, 4410, 4620, 5250, 5460, 6090, 6510, 6930, 7980, 8190, 9030, 9240

Offset: 1

Gilmar Rodriguez Pierluissi (gilmarlily(AT)yahoo.com), Aug 30 2005

nonn

Record value of A023036 or A045917.

a(n)== 0 (mod 30) for n > 13.

Vincenzo Librandi, Table of n, a(n) for n = 1..150
Eric Weisstein's World of Mathematics, Goldbach Partition
Index entries for sequences related to Goldbach conjecture

Essentially the same as A082917. Cf. A082918, A002375, A023036, A045917, A000954.

f[n_] := Length[ Select[n - Prime@ Range@ PrimePi[n/2], PrimeQ]]; t = {}; mxm = -1; Do[ If[ f[n] > mxm, AppendTo[t, n]; mxm = f[n]], {n, 2, 9000, 2}]; t

Edited and extended by Robert G. Wilson v, Sep 08 2005

Changed offset from 0 to 1 by Vincenzo Librandi, Apr 18 2013

cp's OEIS Frontend

A082917 Numbers that can be expressed as the sum of two odd primes in more ways than any smaller even number.

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