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

Author

Hugo Pfoertner, Apr 15 2003

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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 *)