A068531 a(n) = (3^(2^n) - 1)/2^(n + 2).

1, 5, 205, 672605, 14476720225405, 13412827423017626893194723005, 23027704253395670256876704807446325518902757016163752166205, 135750441774555403090761510536778616322479346492704236319926586357457102177506285098634540189560165548644204629442284605

Offset

1,2

Comments

Every element of this sequence is an odd number (see link). - Graeme McRae, Jan 12 2005

More generally, (2*m + 1)^(2^n) == 1 (mod m*(m+1)*2^(n+1)) for n >= 1, and ((2*m + 1)^(2^n) - 1)/(m*(m+1)*2^(n+1)) is an odd number (provided m is not equal to 0 or -1). This is the case m = 1. - Peter Bala, Feb 16 2026

Links

Table of n, a(n) for n=1..8.

Graeme McRae, Proof: for every positive integer k, there exists a positive integer m such that 3^m+5 is divisible by 2^k.

Formula

From Peter Bala, Feb 05 2026: (Start)

a(n) divides a(n+1) and a(n+1)/a(n) = A059917(n).

a(n) = A059723(n)/2. (End)

Mathematica

a[n_] := (3^(2^n) - 1)/2^(n + 2); Array[a, 8] (* Amiram Eldar, May 07 2025 *)

Crossrefs

Cf. A059917, A059723, A068534, A090129, A097421, A199591, A359500.

Sequence in context: A005333 A162087 A292330 * A144139 A020541 A006413

Adjacent sequences: A068528 A068529 A068530 * A068532 A068533 A068534

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 22 2002

Status

approved