A318970 a(1) = 3; for n > 1, a(n) = 2^(a(n-1) - 1) + 5.

3, 9, 261, 1852673427797059126777135760139006525652319754650249024631321344126610074238981

Offset: 1

Author

Max Alekseyev, Sep 06 2018

Keywords

• nonn

Comments

a(n) divides a(n+1) for n <= 4, but it is unknown if this divisibility holds for larger n. In other words, it is unknown if this sequence is a subsequence of A245594.

Modulo any m > 1, the sequence stabilizes within the first A227944(m) <= log_2(m) terms. That is, for any n >= A227944(m), we have a(n) == a(A227944(m)) == A318989(m) (mod m).

It follows that the prime divisors of the terms (cf. A318971) are very sparse: if prime p does not divide any of the first log_2(p) terms, then p does not divide any term.

Links

• Max Alekseyev, Iterations of 2^(n-1)+5: the strong law of small numbers, or something bigger?, MathOverflow, 2016.

Crossrefs

Cf. A245594, A318971, A318989.

Programs

Magma

[n le 1 select 3 else 2^(Self(n-1)-1)+5: n in [1..4]]; // Vincenzo Librandi, Sep 07 2018

Mathematica

RecurrenceTable[{a[1]==3, a[n]==2^(a[n-1] - 1) + 5}, a, {n, 4}] (* Vincenzo Librandi, Sep 07 2018 *)