A362942 Partial sums of A229037.

1, 2, 4, 5, 6, 8, 10, 14, 18, 19, 20, 22, 23, 24, 26, 28, 32, 36, 38, 42, 46, 51, 56, 64, 69, 74, 83, 84, 85, 87, 88, 89, 91, 93, 97, 101, 102, 103, 105, 106, 107, 109, 111, 115, 119, 121, 125, 129, 134, 139, 147, 152, 157, 166, 175, 179, 183, 188, 193

Offset: 1

Author

N. J. A. Sloane, Sep 12 2023

Keywords

• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..100000 (using b-file in A229037)
• N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)

Crossrefs

Cf. A003002, A229037.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{z = 1}, While[Catch[Do[If[z == 2*a[n - k] - a[n - 2*k], Throw@ True], {k, Floor[(n - 1)/2]}]; False], z++]; z]; Accumulate@ Array[a, 120] (* Michael De Vlieger, Sep 12 2023, after Giovanni Resta at A229037 *)

Python

from itertools import count, islice
def A362942_gen(): # generator of terms
    blist, c = [], 0
    for n in count(0):
        i, j, b = 1, 1, set()
        while n-(i<<1) >= 0:
            b.add((blist[n-i]<<1)-blist[n-2*i])
            i += 1
            while j in b:
                j += 1
        blist.append(j)
        yield (c:=c+j)
A362942_list = list(islice(A362942_gen(),30)) # Chai Wah Wu, Sep 12 2023