A122866 - OEIS

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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 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	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: A049449 A104663 A046202 * A097275 A130879 A119741` `Adjacent sequences: A122863 A122864 A122865 * A122867 A122868 A122869`
	KEYWORD	`nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 15 2006`

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Last modified February 16 06:46 EST 2012. Contains 205867 sequences.