cp's OEIS Frontend

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.

A181962 Numbers not of the form pi(p) + pi(sqrt(p)) for some prime p.

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%I A181962 #26 Feb 21 2025 11:17:27
%S A181962 3,6,12,19,35,45,68,80,108,156,173,231,276,297,344,425,504,537,628,
%T A181962 695,726,833,909,1024,1188,1278,1321,1409,1452,1553,1908,2008,2174,
%U A181962 2224,2524,2583,2766,2953,3082,3281,3477,3554,3911,3989,4134,4210,4674,5154,5323
%N A181962 Numbers not of the form pi(p) + pi(sqrt(p)) for some prime p.
%C A181962 Or places of squares in A000430.
%F A181962 a(n) = pi(prime(n)^2) + n = A000879(n) + n. - _Chai Wah Wu_, Feb 18 2025
%e A181962 12 is in the sequence, since pi(23)+pi(sqrt(23))=9+2=11, while pi(29)+pi(sqrt(29))=10+3=13.
%e A181962 Also 12 is in the sequence since A000430(12)=25 is not prime.
%p A181962 a:= n-> numtheory[pi](ithprime(n)^2)+n:
%p A181962 seq(a(n), n=1..50);  # _Alois P. Heinz_, Feb 21 2025
%t A181962 t = Table[PrimePi[n] + PrimePi[Sqrt[n]], {n, Prime[Range[10000]]}]; Complement[Range[t[[-1]]], t] (* _T. D. Noe_, Apr 09 2012 *)
%o A181962 (Python)
%o A181962 from sympy import primepi, prime
%o A181962 def A181962(n): return primepi(prime(n)**2)+n # _Chai Wah Wu_, Feb 18 2025
%Y A181962 Cf. A000430, A000040, A000720, A000879.
%K A181962 nonn
%O A181962 1,1
%A A181962 _Vladimir Shevelev_, Apr 06 2012