

A338946


Lengths of Cunningham chains of the second kind that are sorted by first prime in the chain.


3



3, 2, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 3, 1, 1, 1, 1, 1, 1
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OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

We start with p = 2. Since 2(2)  1 = 3 is prime, and further 2(3)  1 = 5 is prime, but 2(5)  1 is composite, we have chain length 3, so a(1) = 3.
p = 7 is the smallest prime that hasn't appeared in a chain thus far; since 2(7)  1 = 13 is prime but 2(13)  1 = 25 is composite, we have a chain of length 2, so a(2) = 2.
p = 11 is the smallest prime that hasn't appeared in a chain; 2(11)  1 = 21 is composite, so we have a singleton chain, thus a(3) = 1, etc.


MATHEMATICA

Block[{a = {2}, b = {}, j = 0, k, p}, Do[k = Length@ b + 1; If[PrimeQ@ a[[1]], AppendTo[a, 2 a[[1]]  1]; j++, While[! FreeQ[a, Set[p, Prime[k]]], k++]; AppendTo[b, j]; Set[j, 0]; Set[a, Append[a[[1 ;; 2]], p]]], 10^3}; b]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



