A284787 Even numbers representable in at least two ways as the sum of two odd composites.

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

Author

Bernard Schott, Apr 03 2017

Keywords

• nonn

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.

Examples

			30 = 9 + 21 = 15 + 15;
66 = 15 + 51 = 21 + 45.
		

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.

Crossrefs

Cf. A076770, A284788.

Programs

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 *)

Extensions

a(42)-a(57) from Giovanni Resta, Apr 03 2017