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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
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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Apr 15 2003
STATUS
approved