A073672 Rearrangement of natural numbers such that sum of n (n>1) terms starting from the n-th term (included) is a prime.

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, 35, 23, 30, 24, 34, 27, 36, 29, 33, 31, 39, 37, 49, 38, 45, 40, 41, 42, 54, 43, 51, 44, 59, 46, 58, 47, 52, 48, 53, 50, 57, 55, 65, 56, 64, 60, 62, 61, 68, 63, 69, 66, 77, 67, 74, 70

Offset

1,1

Comments

Every 2k-th term is the smallest number which has not been included earlier.

Links

Table of n, a(n) for n=1..72.

Example

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.

Mathematica

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

Crossrefs

The prime sums (see example) are in A075470.

Sequence in context: A320283 A232805 A361740 * A306230 A071065 A359946

Adjacent sequences: A073669 A073670 A073671 * A073673 A073674 A073675

Keyword

nonn

Author

Amarnath Murthy, Aug 11 2002

Status

approved