

A360533


a(n) = index of the diagonal of the natural number array, A000027, that includes prime(n). See Comments.


0



1, 1, 0, 3, 4, 0, 3, 1, 4, 7, 3, 8, 0, 4, 7, 5, 4, 0, 11, 3, 1, 12, 4, 8, 3, 5, 9, 12, 8, 0, 3, 5, 16, 12, 8, 12, 11, 1, 9, 16, 4, 0, 19, 15, 7, 3, 20, 4, 12, 16, 19, 7, 3, 17, 16, 4, 8, 12, 23, 15, 11, 9, 12, 4, 0, 8, 15, 3, 17, 21
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OFFSET

1,4


COMMENTS

The natural number array, A000027 = (w(n,k)) = (n + (n + k  2) (n + k  1)/2), has corner:
1 2 4 7 ...
3 5 8 12 ...
6 9 13 18 ...
10 14 19 25 ...
The indexing of diagonals is given in A191360. Conjecture: Every oddindexed diagonal contains infinitely many primes.


LINKS



EXAMPLE

Prime(1) = 2 is in the diagonal (w(n,n+1)), so a(1) = 1.
Prime(13) = 43 is in the diagonal (w(n,n4)), so a(7) = 4.


MATHEMATICA

Map[1 + #[[1]]  2 #[[2]] &[{#[[2]], #[[1]]  ((#[[2]]  1) + (#[[2]]  1)^2)/
2} &[{#, Floor[(1 + Sqrt[8 #  7])/2]}] &[Prime[#]]] &, Range[1000]]


CROSSREFS



KEYWORD

easy,sign


AUTHOR



STATUS

approved



