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A366911 a(n) = (A364054(n+1) - A364054(n)) / prime(n) (where prime(n) denotes the n-th prime number).

%I A366911 #17 Mar 04 2024 19:48:02
%S A366911 1,1,1,-1,1,-1,1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,1,1,-3,
%T A366911 2,-2,1,-1,1,-1,2,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,
%U A366911 -1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1
%N A366911 a(n) = (A364054(n+1) - A364054(n)) / prime(n) (where prime(n) denotes the n-th prime number).
%C A366911 a(n) is the number of steps of size prime(n) in going from A364054(n) to A364054(n+1).
%H A366911 N. J. A. Sloane, <a href="/A366911/b366911.txt">Table of n, a(n) for n = 1..9999</a>
%H A366911 Rémy Sigrist, <a href="/A366911/a366911.gp.txt">PARI program</a>
%e A366911 a(7) = (A364054(8) - A364054(7)) / prime(7) = (19 - 2) / 17 = 1.
%t A366911 nn = 2^16; c[_] := False; m[_] := 0; j = 1; c[0] = c[1] = True;
%t A366911   Monitor[Do[p = Prime[n - 1]; r = Mod[j, p];
%t A366911     While[Set[k, p m[p] + r ]; c[k], m[p]++];
%t A366911     Set[{a[n - 1], c[k], j}, {(k - j)/p, True, k}], {n, 2, nn + 1}], n];
%t A366911 Array[a, nn] (* _Michael De Vlieger_, Oct 27 2023 *)
%o A366911 (PARI) See Links section.
%o A366911 (Python)
%o A366911 from itertools import count, islice
%o A366911 from sympy import nextprime
%o A366911 def A366911_gen(): # generator of terms
%o A366911     a, aset, p = 1, {0,1}, 2
%o A366911     while True:
%o A366911         k, b = divmod(a,p)
%o A366911         for i in count(-k):
%o A366911             if b not in aset:
%o A366911                 aset.add(b)
%o A366911                 a, p = b, nextprime(p)
%o A366911                 yield i
%o A366911                 break
%o A366911             b += p
%o A366911 A366911_list = list(islice(A366911_gen(),30)) # _Chai Wah Wu_, Oct 27 2023
%Y A366911 Cf. A160357, A364054, A366912 (partial sums).
%K A366911 sign
%O A366911 1,29
%A A366911 _Rémy Sigrist_, Oct 27 2023