

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
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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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



