A347309 a(n) = gcd(b(n-1)+1, b(n)), where b is A347113.

2, 5, 11, 23, 47, 5, 2, 3, 7, 3, 4, 3, 13, 9, 5, 2, 19, 13, 7, 8, 17, 5, 3, 5, 31, 21, 11, 3, 4, 3, 37, 25, 2, 29, 59, 17, 3, 2, 41, 83, 167, 5, 3, 2, 43, 29, 2, 3, 7, 19, 5, 23, 2, 3, 5, 61, 41, 7, 2, 53, 107, 43, 11, 7, 2, 67, 3, 4, 5, 71, 13, 3, 2, 3, 73, 3, 5, 2, 79, 53, 2, 7

Offset: 2

Author

N. J. A. Sloane, Sep 01 2021

Keywords

• nonn

Comments

The definition of A347113 forbids a(n) to be 1.

Links

• Michel Marcus, Table of n, a(n) for n = 2..10000 (terms 2..1000 from N. J. A. Sloane)

Crossrefs

Cf. A347113.

Programs

Maple

b:= proc() true end:
g:= proc(n) option remember; local j, k; j:= g(n-1)+1;
      for k from 2 do if b(k) and k<>j and igcd(k, j)>1
        then b(k):= false; return k fi od
    end: g(1):= 1:
a:= n-> igcd(g(n-1)+1, g(n)):
seq(a(n), n=2..100);  # Alois P. Heinz, Sep 02 2021

Mathematica

b[_] = True;
g[n_] := g[n] = Module[{j = g[n - 1] + 1, k},
     For[k = 2, True, k++, If[ b[k] && k != j && GCD[k, j] > 1,
          b[k] = False; Return[k]]]];
g[1] = 1;
a[n_] := GCD[g[n - 1] + 1, g[n]];
Table[a[n], {n, 2, 100}] (* Jean-François Alcover, May 06 2022, after Alois P. Heinz *)