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A082917 Numbers that can be expressed as the sum of two odd primes in more ways than any smaller even number. 5
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 (list; graph; refs; listen; history; text; internal format)
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

T. D. Noe, Table of n, a(n) for n = 1..244

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

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Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)