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

Author

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

Keywords

• nonn

Examples

			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, ...,.
		

Links

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

Crossrefs

Cf. A054408, A121861, A121862, A122867.

Programs

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}]

Extensions

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