OFFSET

1,1

COMMENTS

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

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

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Nov 16 2021

STATUS

approved