A377897 Numbers k such that k + PrimePi(k) is even.
4, 5, 8, 10, 11, 14, 16, 17, 20, 22, 23, 25, 27, 30, 31, 33, 35, 38, 40, 41, 44, 46, 47, 49, 51, 54, 56, 58, 59, 62, 64, 66, 67, 69, 72, 73, 75, 77, 80, 82, 83, 85, 87, 90, 92, 94, 96, 97, 99, 102, 103, 105, 108, 109, 111, 114, 116, 118, 120, 122, 124, 126, 127, 129, 132, 134, 136, 137, 140
Offset: 1
Keywords
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Select[Range[200], EvenQ[# + PrimePi[#]] &] (* Paolo Xausa, Nov 13 2024 *)
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Python
from sympy import nextprime def A377897_gen(): # generator of terms p,q,a = 3,5,1 while True: yield from range(p+a,q,2) p, q, a = q, nextprime(q), a^1 A377897_list = list(islice(A377897_gen(),69)) # Chai Wah Wu, Nov 13 2024
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Python
from sympy import primepi, prevprime def A377897(n): def f(x): if x<=3: return n+x p = prevprime(x+1) i = int(primepi(p)) return n+x-(p>>1)-(x-p-((i^x)&1)>>1) m, k = n, f(n) while m != k: m, k = k, f(k) return m # Chai Wah Wu, Nov 13 2024