A377897 - OEIS

%I #20 Nov 14 2024 05:31:41

%S 4,5,8,10,11,14,16,17,20,22,23,25,27,30,31,33,35,38,40,41,44,46,47,49,

%T 51,54,56,58,59,62,64,66,67,69,72,73,75,77,80,82,83,85,87,90,92,94,96,

%U 97,99,102,103,105,108,109,111,114,116,118,120,122,124,126,127,129,132,134,136,137,140

%N Numbers k such that k + PrimePi(k) is even.

%H Paolo Xausa, <a href="/A377897/b377897.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[200], EvenQ[# + PrimePi[#]] &] (* _Paolo Xausa_, Nov 13 2024 *)

%o (Python)

%o from sympy import nextprime

%o def A377897_gen(): # generator of terms

%o     p,q,a = 3,5,1

%o     while True:

%o         yield from range(p+a,q,2)

%o         p, q, a = q, nextprime(q), a^1

%o A377897_list = list(islice(A377897_gen(),69)) # _Chai Wah Wu_, Nov 13 2024

%o (Python)

%o from sympy import primepi, prevprime

%o def A377897(n):

%o     def f(x):

%o         if x<=3: return n+x

%o         p = prevprime(x+1)

%o         i = int(primepi(p))

%o         return n+x-(p>>1)-(x-p-((i^x)&1)>>1)

%o     m, k = n, f(n)

%o     while m != k: m, k = k, f(k)

%o     return m # _Chai Wah Wu_, Nov 13 2024

%Y Cf. A000720, A121053, A377994 (complement).

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 13 2024