

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.


1



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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..88.


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


CROSSREFS

Cf. A054408, A121861, A121862, A122866.
Sequence in context: A288638 A261494 A168377 * A124775 A140075 A099555
Adjacent sequences: A122864 A122865 A122866 * A122868 A122869 A122870


KEYWORD

nonn,tabl


AUTHOR

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


STATUS

approved



