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A284787
Even numbers representable in at least two ways as the sum of two odd composites.
2
30, 36, 42, 48, 50, 54, 58, 60, 64, 66, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162
OFFSET
1,1
COMMENTS
If n is even and n > 68, at least two of n-15, n-25, n-35, n-45, n-55, n-65, are odd numbers divisible by 3 and greater than 3, with n = (n-55) + 55 for example.
So if n is even and n > 68, then n can be written in at least two ways as the sum of two odd positive composite numbers.
REFERENCES
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, 1997, page 111.
LINKS
R. E. Ruemmler and Minnich, Problem 1328: Sums of Composite Odd Numbers, Mathematics Magazine, 63 (1990), 276.
EXAMPLE
30 = 9 + 21 = 15 + 15;
66 = 15 + 51 = 21 + 45.
MATHEMATICA
up = 200; oddco = Select[Range[9, up, 2], ! PrimeQ[#] &]; Select[ Range[2, up, 2], Length@ Quiet@ IntegerPartitions[#, {2}, oddco, 2] == 2 &] (* Giovanni Resta, Apr 03 2017 *)
CROSSREFS
Sequence in context: A257447 A257440 A114840 * A214408 A350353 A357874
KEYWORD
nonn
AUTHOR
Bernard Schott, Apr 03 2017
EXTENSIONS
a(42)-a(57) from Giovanni Resta, Apr 03 2017
STATUS
approved