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

1,2

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.)

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 *)

Prog

(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

Crossrefs

Cf. A003002, A229037.

Sequence in context: A276603 A175416 A190854 * A069872 A216163 A371182

Adjacent sequences: A362939 A362940 A362941 * A362943 A362944 A362945

Keyword

nonn

Author

N. J. A. Sloane, Sep 12 2023

Status

approved