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

1,1

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A157037 A189992 A255746 * A001172 A339437 A108605

Adjacent sequences: A082914 A082915 A082916 * A082918 A082919 A082920

Keyword

nonn

Author

Hugo Pfoertner, Apr 15 2003

Status

approved