A178915 Rearrangement of natural numbers so that every partial sum is composite.

4, 2, 3, 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Amarnath Murthy, Jun 23 2010

Keywords

• easy
• nonn

Comments

a(n) = n for n > 4.

Except for the integers 1 & 4 which are interchanged, the sequence is in order. Proof: Except for the first three triangular numbers (A000217), {0, 1, 3}, they are all composite. - Robert G. Wilson v, Jun 27 2010

Examples

			Partial sums are 4,6,9,10,15,21,...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2, -1).

Programs

Mathematica

f[s_List] := Block[{k = 0, t = Plus @@ s}, While[MemberQ[s, k] || PrimeQ[t + k] || t + k < 2, k++ ]; Append[s, k]]; Rest@ Nest[f, {0}, 72] (* Robert G. Wilson v, Jun 27 2010 *)

Formula

G.f.: 3 - 3*x^3 + 1/(x-1)^2. - Sergei N. Gladkovskii, Oct 16 2012

Extensions

a(40)-a(72) from Robert G. Wilson v, Jun 27 2010