A349411 a(n) = prime j = A347113(i)-1 in order of appearance.

2, 5, 11, 23, 47, 3, 7, 13, 19, 17, 31, 37, 29, 59, 41, 83, 167, 43, 61, 53, 107, 67, 71, 73, 79, 89, 179, 359, 719, 1439, 2879, 97, 101, 103, 109, 113, 227, 131, 263, 127, 139, 137, 151, 157, 149, 163, 181, 173, 347, 191, 383, 199, 193, 211, 197, 223, 229, 233

Offset

1,1

Comments

Let s = A347113, j = s(i)+1 and k = s(i+1). We recall the 3 constraints presented in A347113:

1. j = k is forbidden.

2. gcd(j,k) = 1 is forbidden.

3. All terms in s are distinct.

These constraints confine prime j to the relationship j | k, since gcd(j,k)=1 and j=k is forbidden. In the context of s, j | k implies j < k and sequence increase. The least k > j such that j | k is 2j, giving rise to Cunningham chains of the first kind.

Links

Table of n, a(n) for n=1..58.

Chris Caldwell's Prime Glossary, Cunningham chains.

Michael De Vlieger, Log-log scatterplot of a(n), n=1..2^19, indicating prime j in red.

Michael De Vlieger, Extended table of n, a(n) for n=1..45450

Eric Weisstein's World of Mathematics, Cunningham Chain.

Example

s(1) = 1, thus j = s(1)+1 = 2, which is prime, therefore a(1) = 2.
s(2) = 4; j = 5, thus a(2) = 5, etc.

Mathematica

c[_] = 0; j = m = 2; m = 1 + {1}~Join~Reap[Do[If[IntegerQ @Log2[i], While[c[m] > 0, m++]]; Set[k, m]; While[Or[c[k] > 0, k == j, GCD[j, k] == 1], k++]; Sow[k]; Set[c[k], i]; j = k + 1, {i, 239}]][[-1, -1]]; Select[m, PrimeQ]]

Crossrefs

Cf. A347113, A348779, A349412.

Sequence in context: A093053 A192580 A075712 * A347309 A174162 A340799

Adjacent sequences: A349408 A349409 A349410 * A349412 A349413 A349414

Keyword

nonn

Author

Michael De Vlieger, Nov 16 2021

Status

approved