A338945 Lengths of Cunningham chains of the first kind that are sorted by first prime in the chain.

5, 2, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1

Offset

1,1

Comments

Row lengths of A075712.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Chris K. Caldwell, Cunningham Chain (PrimePages, Prime Glossary).

Wikipedia, Cunningham chain.

Example

We begin with the smallest prime 2. Since 2(5) + 1 = 11 is prime, further, 2(11) + 1 = 23, 2(23) + 1 = 47 are prime but 2(47) + 1 = 95 is not, we have the complete chain {2, 5, 11, 23, 47} of length 5, thus a(1) = 5.
We resume with 3, since 3 has not appeared in any chain generated thus far. Since 2(3) + 1 = 7, but 2(7) + 1 = 15, we have the complete chain {3, 7}, therefore a(2) = 2.
Starting from 13, we find 2(13) + 1 = 27, thus we have a singleton chain and have 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

Cf. A075712, A338944, A338946.

Sequence in context: A113103 A033325 A126690 * A263007 A104714 A085119

Adjacent sequences: A338942 A338943 A338944 * A338946 A338947 A338948

Keyword

nonn

Author

Michael De Vlieger, Nov 17 2020

Status

approved