A122867 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 that array read by successive antidiagonals.

2, 1, 1, 1, 3, 4, 2, 2, 2, 6, 1, 6, 6, 4, 10, 2, 2, 8, 8, 6, 8, 1, 4, 4, 4, 4, 12, 12, 4, 4, 6, 6, 14, 14, 8, 16, 3, 2, 2, 12, 12, 10, 10, 10, 14, 2, 2, 6, 6, 8, 8, 12, 12, 14, 24, 1, 6, 4, 10, 10, 10, 10, 20, 20, 18, 30, 2, 2, 12, 6, 8, 8, 14, 14, 18, 18, 22, 22, 1, 4, 4, 8, 8, 16, 16, 18, 18, 16

Offset: 1

Author

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

Keywords

• nonn
• tabl

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, ...,.
		

Crossrefs

Cf. A054408, A121861, A121862, A122866.

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[k, n - k], {n, 13}, {k, n}] // Flatten