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 A178915 Rearrangement of natural numbers so that every partial sum is composite. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS FORMULA G.f.: 3 - 3*x^3 + 1/(x-1)^2. - Sergei N. Gladkovskii, Oct 16 2012 EXAMPLE Partial sums are 4,6,9,10,15,21,... 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 *) CROSSREFS Sequence in context: A231169 A297847 A145326 * A222221 A254043 A016513 Adjacent sequences:  A178912 A178913 A178914 * A178916 A178917 A178918 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Jun 23 2010 EXTENSIONS a(40)-a(72) form Robert G. Wilson v, Jun 27 2010 STATUS approved

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Last modified December 10 12:43 EST 2019. Contains 329896 sequences. (Running on oeis4.)