A090533 Duplicate of A025003.
2, 4, 8, 14, 22, 33, 48, 66, 90, 120, 156, 202, 256, 322, 400, 494, 604, 734, 888, 1067
Offset: 1
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
c = q = 0; w = {}; Do[Set[a[i], If[PrimeQ[i], c++, a[i - c]]]; q++; If[a[i] == 0, AppendTo[w, q]; q = 0], {i, 2, 10^5}]; Most[w] (* Michael De Vlieger, Nov 04 2021 *)
from sympy import primepi
def depth(k):
d = 0
while k > 1:
k -= primepi(k)
d += 1
return d
m = 1
for n in range (0, 101):
a = 0
while depth(m + a) == n:
a += 1
print(a)
m += a
a(1) = 0 because f^0(1) = 1; a(2) = 1 because f(2) = 2 + pi(2) - pi(2 + pi(2)) = 1; a(4) = 3 because f^3(4) = f^2(f(4)) = f^2(3) = f(f(3)) = f(2) = 1.
a:= proc(n) option remember; `if`(n=1, 0, 1+a((
pi-> n+pi(n)-pi(n+pi(n)))(numtheory[pi])))
end:
seq(a(n), n=1..80); # Alois P. Heinz, Oct 24 2020
f[n_] := Module[{x = n + PrimePi[n]}, x - PrimePi[x]];
a[n_] := Module[{nb = 0, m = n}, While[m != 1, m = f[m]; nb++]; nb];
Array[a, 100] (* Jean-François Alcover, Oct 24 2020, after PARI code *)
f(n) = {my(x = n + primepi(n)); x - primepi(x);} \\ A337978
a(n) = {my(nb=0); while (n != 1, n = f(n); nb++); nb;} \\ Michel Marcus, Oct 06 2020
from sympy import primepi
print(0)
n = 2
for n in range (2, 10000001):
ct = 0
n_l = n
pi_l = primepi(n)
while ct >= 0:
n_r = n_l + pi_l
pi_r = primepi(n_r)
n_l = n_r - pi_r
pi_l = primepi(n_l)
ct += 1
if n_l == 1:
print(ct)
break
a(10) = 3, 10 ->6 ->3 ->1. a(100) = 9. f(100) =100-25 = 75, f(75) = 75-21= 54, f(54) = 54-16 = 38, f(38) = 38-12= 26, f(26) = 26-9 = 17, f(17) = 17-7 = 10, f(10) = 10-4 =6, f(6) = 6-3=3, f(3) = 3-2 =1.
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