A238269 Smallest number that can be written in n ways as the sum of two numbers of the form p or 2p, where p is prime.

4, 6, 8, 16, 24, 33, 36, 63, 48, 60, 93, 140, 84, 108, 132, 189, 165, 144, 120, 210, 297, 168, 204, 180, 276, 252, 285, 288, 462, 240, 372, 432, 336, 300, 396, 609, 360, 492, 552, 468, 564, 528, 576, 504, 708, 1089, 648, 480, 420, 540, 768, 672, 600, 816, 792

Offset: 1

Author

Lei Zhou, Feb 21 2014

Keywords

• nonn

Examples

			4 is the smallest number that can be written in only one way as the sum of two primes or doubled primes, 4=2+2. So a(1)=4;
6 = 2+2*2 = 3+3, two ways, so a(2)=6;
...
33 = 2+31 = 2*2+29 = 7+2*13 = 2*5+23 = 11+2*11 = 2*7+19, 6 ways.  And all numbers smaller than 33 can only be split in 5 or fewer ways.  So a(6)=33.
		

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001751, A002375, A103151, A238268.

Programs

Mathematica

target = 55; n = 3; a = {}; sc = 0; Do[AppendTo[a, 0], {i, 1, target}]; While[sc < target, n++; ct = 0; Do[If[((PrimeQ[i]) || (PrimeQ[i/2])) && ((PrimeQ[n - i]) || (PrimeQ[(n - i)/2])), ct++], {i, 2, Floor[n/2]}]; If[ct<=target,If[a[[ct]] == 0, a[[ct]] = n; sc++]]];a