%I #2 Dec 05 2013 19:55:31
%S 2,1,4,3,6,5,9,7,10,8,14,11,12,13,22,15,26,16,20,17,25,18,28,19,32,21,
%T 35,23,30,24,34,27,36,29,33,31,39,37,49,38,45,40,41,42,54,43,51,44,59,
%U 46,58,47,52,48,53,50,57,55,65,56,64,60,62,61,68,63,69,66,77,67,74,70
%N Rearrangement of natural numbers such that sum of n (n>1) terms starting from the n-th term (included) is a prime.
%C Every 2k-th term is the smallest number which has not been included earlier.
%e a(1) = 2, a(2)=1, 1+4 = 5 which is prime; a(3) = 4, 4+3+6 = 13 which is prime; a(4) = 3, 3+6+5+9 = 23 which is prime; etc.
%t a = {2, 1, 4}; f[n_] := Block[{k = 1, b = Take[a, {n, 2n - 3}]}, While[ Position[a, k] != {}, k++ ]; b = Append[b, k]; a = Append[a, k]; While[ Position[a, k] != {} || !PrimeQ[Plus @@ b + k], k++ ]; a = Append[a, k]]; Do[ f[n], {n, 3, 40}]; a
%Y The prime sums (see example) are in A075470.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Aug 11 2002
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