A094591 a(0) = 1; a(n) = n + (largest element of {a} <= n).

1, 2, 4, 5, 8, 10, 11, 12, 16, 17, 20, 22, 24, 25, 26, 27, 32, 34, 35, 36, 40, 41, 44, 45, 48, 50, 52, 54, 55, 56, 57, 58, 64, 65, 68, 70, 72, 73, 74, 75, 80, 82, 83, 84, 88, 90, 91, 92, 96, 97, 100, 101, 104, 105, 108, 110, 112, 114, 116, 117, 118, 119, 120, 121, 128, 130

Offset: 0

Author

Leroy Quet, Jun 07 2004

Keywords

• nonn
• easy

Comments

A self-describing sequence. Pick any number n; this n says: "There are n terms in the sequence which are < 2n". This sequence is the slowest increasing one with this property. See comments on A037988. - Eric Angelini, Jun 15 2007

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Jon Maiga, Computer-generated formulas for A094591, Sequence Machine.

Crossrefs

Cf. A037988, A272729.

Programs

Mathematica

Block[{a = {1}}, Do[AppendTo[a, i + Last@ TakeWhile[a, # <= i &]], {i, 65}]; a] (* Michael De Vlieger, Sep 04 2017 *)

Python

def aupton(nn):
    alst = [1]
    for n in range(1, nn+1):
        alst.append(n + max(k for k in alst if k <= n))
    return alst
print(aupton(65)) # Michael S. Branicky, Oct 28 2021

Formula

From Andrey Zabolotskiy, Oct 28 2021: (Start)

a(n) = A037988(n-1) + 1. [Conjectured by the original author, apparently proved by Eric Angelini.]

The first differences are A272729. [discovered by Sequence Machine] (End)

Extensions

More terms from Vladeta Jovovic, Jun 11 2004