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A366912
Partial sums of A366911: a(1) = 0, and for n > 0, a(n+1) = a(n) + A366911(n).
3
0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 7, 8, 5, 7, 5, 6, 5, 6, 5, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 6, 7, 8, 9, 8, 9, 8
OFFSET
1,3
COMMENTS
By analogy with A064289, a(n) corresponds to the height of A364054(n) = number of addition steps - number of subtraction steps to produce it.
LINKS
Rémy Sigrist, Colored scatterplot of the first 100000 terms of A364054 (where the color is function of a(n))
Rémy Sigrist, PARI program
FORMULA
a(n) = Sum_{k = 1..n-1} A366911(k).
EXAMPLE
a(5) = A366911(1) + A366911(2) + A366911(3) + A366911(4) = 1 + 1 + 1 - 1 = 2.
MATHEMATICA
nn = 2^16; c[_] := False; m[_] := 0; j = 1; s = b[1] = 0;
c[0] = c[1] = True;
Monitor[Do[p = Prime[n - 1]; r = Mod[j, p];
While[Set[k, p m[p] + r ]; c[k], m[p]++]; s += (k - j)/p;
Set[{a[n - 1], b[n - 1], c[k], j}, {(k - j)/p, s, True, k}],
{n, 2, nn + 1}], n];
Array[b, nn] (* Michael De Vlieger, Oct 27 2023 *)
PROG
(PARI) See Links section.
(Python)
from itertools import count, islice
from sympy import nextprime
def A366912_gen(): # generator of terms
a, aset, p, c = 1, {0, 1}, 2, 0
while True:
k, b = divmod(a, p)
for i in count(-k):
if b not in aset:
aset.add(b)
a, p = b, nextprime(p)
yield c
c += i
break
A366912_list = list(islice(A366912_gen(), 30)) # Chai Wah Wu, Oct 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Oct 27 2023
STATUS
approved