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

1,1

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

Table of n, a(n) for n=1..57.

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

Cf. A076770, A284788.

Sequence in context: A257447 A257440 A114840 * A214408 A350353 A357874

Adjacent sequences: A284784 A284785 A284786 * A284788 A284789 A284790

Keyword

nonn

Author

Bernard Schott, Apr 03 2017

Extensions

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

Status

approved