

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 recordsetting 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, k1], 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]]] (* JeanFrançois 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



