A122866 Consider the array of sequences defined to be "the least previously nonoccurring positive integer such that partial sum + k is prime" beginning with k=0. This sequence is the main diagonal of that array.

2, 3, 6, 4, 12, 10, 16, 12, 16, 24, 26, 24, 30, 28, 28, 44, 36, 42, 20, 38, 34, 54, 54, 56, 48, 44, 50, 52, 68, 56, 56, 60, 62, 66, 66, 70, 76, 84, 76, 58, 92, 90, 88, 90, 80, 88, 92, 102, 104, 102, 114, 104, 108, 98, 114, 108, 92, 100, 120, 126, 124, 130, 126, 142, 116, 126

Offset

0,1

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Example

The array of sequences begins
k= 0: 2, 1, 4, 6, 10, 8, 12, 16, 14, 24, 30, 22, 18, 26, 34, ...,.
k= 1: 1, 3, 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, ...,.
k= 2: 1, 2, 6, 8, 4, 14, 10, 12, 20, 18, 16, 24, 26, 28, 32, ...,.
k= 3: 2, 6, 8, 4, 14, 10, 12, 20, 18, 16, 24, 26, 28, 32, 34, ...,.
k= 4: 1, 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, 32, ...,.
k= 5: 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, 32, 28, ...,.

Mathematica

f[s_] := Append[s, k = 1; p = q + Plus @@ s; While[MemberQ[s, k] || !PrimeQ[p + k], k++ ]; k]; T[n_, k_] := Nest[q = k; f, {}, n][[ -1]]; Table[T[n, n - 1], {n, 66}]

Crossrefs

Cf. A054408, A121861, A121862, A122867.

Sequence in context: A225642 A273317 A328443 * A097275 A130879 A119741

Adjacent sequences: A122863 A122864 A122865 * A122867 A122868 A122869

Keyword

nonn

Author

Jonathan Vos Post and Robert G. Wilson v, Sep 15 2006

Extensions

Offset changed to 0 by Chai Wah Wu, Aug 27 2017

Status

approved