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A073946 Squares k such that k + pi(k) is a prime.

%I A073946 #19 May 07 2021 12:52:35
%S A073946 9,36,81,121,361,625,961,3136,6724,8281,9604,10609,12996,13225,19881,
%T A073946 25281,38025,39204,40000,43264,44944,45796,47961,60516,64009,79524,
%U A073946 80089,80656,83521,86436,90000,93636,103684,117649,121801,129600
%N A073946 Squares k such that k + pi(k) is a prime.
%H A073946 Robert Israel, <a href="/A073946/b073946.txt">Table of n, a(n) for n = 1..1000</a>
%e A073946 a(1)=9, since 9 is a square, pi(9)=4 and 9+4=13 is a prime.
%p A073946 select(t -> isprime(t + numtheory:-pi(t)), [seq(i^2,i=1..1000)]); # _Robert Israel_, Mar 21 2017
%t A073946 Select[Range[1000]^2, PrimeQ[# + PrimePi[#]] &] (* _Indranil Ghosh_, Mar 21 2017 *)
%o A073946 (PARI)
%o A073946 v=vector(1000);
%o A073946 for(n=1, 1000, v[n] = n^2);
%o A073946 for(n=1, 1000, if(isprime(v[n] + primepi(v[n])), print1(v[n],", "))) \\ _Indranil Ghosh_, Mar 21 2017
%o A073946 (Python)
%o A073946 from sympy import primepi, isprime
%o A073946 N = (x**2 for x in range(1, 1001))
%o A073946 print([n for n in N if isprime(n + primepi(n))]) # _Indranil Ghosh_, Mar 21 2017
%Y A073946 This sequence is a subsequence of sequence A077510. The corresponding sequence of primes is A113943 and the square roots of the original sequence is A113944.
%K A073946 nonn
%O A073946 1,1
%A A073946 _David Garber_, Nov 13 2002