A318971 -id:A318971 - cp's OEIS frontend

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

3, 9, 261, 1852673427797059126777135760139006525652319754650249024631321344126610074238981

Offset: 1

Max Alekseyev, Sep 06 2018

nonn

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.

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

Cf. A245594, A318971, A318989.

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

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

A318989 Limiting value of A318970(k) mod n as k grows.

Original entry on oeis.org

0, 1, 0, 1, 1, 3, 2, 5, 0, 1, 6, 9, 1, 9, 6, 5, 4, 9, 14, 1, 9, 17, 14, 21, 6, 1, 18, 9, 0, 21, 6, 5, 6, 21, 16, 9, 2, 33, 27, 21, 6, 9, 3, 17, 36, 37, 19, 21, 16, 31, 21, 1, 6, 45, 6, 37, 33, 29, 34, 21, 52, 37, 9, 5, 1, 39, 40, 21, 60, 51, 42, 45, 42, 39, 6, 33, 72, 27, 28, 21, 72, 47, 56, 9, 21, 3, 0, 61, 37, 81, 79, 37, 6, 19, 71, 69, 11, 65, 72, 81

Offset: 1

Max Alekseyev, Sep 06 2018

nonn

Is there a prime p in A318971 such that a(p) is nonzero?

Cf. A245970, A254410, A254411, A318970, A318971.

a(n) = A318970(k) mod n holds for any k >= A227944(n). In particular, a(n) = A318970(A227944(n)) mod n.

cp's OEIS Frontend

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

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