cp's OEIS Frontend

The corresponding record values are 2,4,6,7,8,9,10,12,13,14.

From David A. Corneth, Nov 10 2018: (Start)

Terms a(n) are of the form 3*k+2 for n > 1.

If 2^k - 1 is composite then a(n) is not divisible by any prime factor of 2^k-1 for n > k. So for example, gcd(a(n), 105) = 1 for n > 5. (End)

From Glen Whitney, Sep 14 2022: (Start)

Similarly to Corneth's observations, modulo any prime p, any residue for a(n) of the form 2^k - 1 mod p is forbidden for n greater than or equal to the number of such residues; for example a(n) may not be congruent to 0, 1, or 3 mod 7 for n >= 3.

For n > 2, if a(n) appears in this sequence, 2a(n) + 1 must appear in A057331. (End)

For n > 10, a(n) == -1 (mod 2*3*5*11*13). - Farideh Firoozbakht, Apr 24 2004

From Glen Whitney, Sep 14 2022: (Start)

Extending Firoozbakht's observation, modulo any prime p, all residues of a(n) of the form 2^k - 1 mod p are forbidden for n greater than or equal to the number of such residues, e.g., a(n) may not be congruent to 1 or 3 mod 7 for n >= 2.

A067849(a(n)) >= n and for each odd a(n) that occurs in this sequence, (a(n)-1)/2 occurs in A321058. (End)