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.
with(numtheory): A090405:=n->pi(n+2)-pi(n): seq(A090405(n), n=1..150); # Wesley Ivan Hurt, Mar 30 2017
Table[Subtract @@ Map[PrimePi, n + {2, 0}], {n, 120}] (* or *)
Table[Boole@ PrimeQ[n + 1 + Boole[OddQ@ n]] + Boole[n == 1], {n, 120}] (* Michael De Vlieger, Mar 30 2017 *)
for(n=1, 100, print1(primepi(n + 2) - primepi(n),", ")) \\ Indranil Ghosh, Mar 31 2017
from sympy import primepi print([primepi(n + 2) - primepi(n) for n in range(1, 101)]) # Indranil Ghosh, Mar 31 2017
from sympy import isprime
def a(n):
if n<2: return 2
else:
if isprime(n + 1 + (n%2 == 1) + (n==1)): return 1
else: return 0 # Indranil Ghosh, Mar 31 2017
B:= [seq(numtheory:-pi(n),n=1..103)]: B[4..-1] - B[1..-4]; # Robert Israel, Aug 14 2015
Last[#]-First[#]&/@Partition[PrimePi[Range[110]],4,1] (* Harvey P. Dale, Feb 24 2013 *)
a:= proc(n) option remember; `if`(n=0, 1, a(n-1)+
add(`if`(isprime(j), a(n-j), 0), j=3..n))
end:
seq(a(n), n=0..42); # Alois P. Heinz, Aug 12 2019
nmax = 42; CoefficientList[Series[1/(1 - x - Sum[x^Prime[k], {k, 2, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Boole[PrimeOmega[k] < 2 && OddQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 42}]
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