

A334404


a(0)=0; for n>0, a(n) is an integer not previously seen such that the sum of all previous terms plus a(n) equals the smallest prime number not yet created by any previous sum.


0



0, 2, 1, 4, 2, 6, 8, 6, 10, 14, 20, 12, 18, 16, 22, 12, 20, 18, 16, 24, 10, 28, 34, 30, 26, 32, 24, 34, 4, 40, 60, 38, 36, 56, 44, 14, 42, 48, 26, 54, 72, 52, 48, 66, 50, 42, 46, 30, 60, 90, 62, 36, 58, 52, 64, 22, 8, 74, 38, 68, 54, 66, 78, 76, 70, 82, 46
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OFFSET

0,2


COMMENTS

See A175499 for an equivalent sequence which sums to the smallest positive integer not yet created.


LINKS

Table of n, a(n) for n=0..66.


EXAMPLE

a(1) = 2 as the sum of all previous terms plus a(1) = 0 + 2 = 2, where 2 has not previously occurred in the sequence and the prime 2 has not been previously created.
a(2) = 1 as the sum of all previous terms plus a(2) = 0 + 2 + 1 = 3, where 1 has not previously occurred in the sequence and the prime 3 has not been previously created.
a(3) = 4 as the sum of all previous terms plus a(3) = 0 + 2 + 1 + 4 = 7, where 4 has not previously occurred in the sequence and the prime 7 has not been previously created. Note that the next smallest uncreated prime after a(2) is 5 but that would require a(3) = 2 which is not allowed as a(1) = 2.
a(4) = 2 as the sum of all previous terms plus a(4) = 0 + 2 + 1 + 4  2 = 5, where 2 has not previously occurred in the sequence and the prime 5 has not been previously created.


MATHEMATICA

Nest[Block[{k = 1, s = Total[#[[All, 1]] ], i = 1, p}, While[Nand[FreeQ[#[[All, 1]], Set[p, Prime@ i]], FreeQ[#[[All, 1]], p  s] ], i++]; While[Nand[FreeQ[#[[All, 1]], k], k + s == p], If[k < 0, Set[k, k + 1], k *= 1]]; Append[#, {k, p}]] &, {{0, 0}}, 66][[All, 1]] (* Michael De Vlieger, Sep 11 2020 *)


CROSSREFS

Cf. A175499, A000040, A000217.
Sequence in context: A330001 A292402 A205685 * A143375 A339418 A074364
Adjacent sequences: A334401 A334402 A334403 * A334405 A334406 A334407


KEYWORD

sign


AUTHOR

Scott R. Shannon, Sep 08 2020


STATUS

approved



