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Primes p with same last four digits as pi(p).
2

%I #36 Jul 16 2021 14:24:29

%S 99551,165103,208697,263071,284833,588229,663853,728681,1073819,

%T 1181617,1213909,1407647,1515259,1590487,1676497,2116991,2170681,

%U 2202857,2417477,2481833,2589143,2664229

%N Primes p with same last four digits as pi(p).

%H Robert Israel and Charles R Greathouse IV, <a href="/A232188/b232188.txt">Table of n, a(n) for n = 1..10000</a> (first 607 terms from Israel)

%F a(n) = prime(A232189(n)).

%e 15103 and prime(15103)=165103, both end with 5103.

%p Primes:= select(isprime, [2,seq(2*i+1, i=1..10^6)]):

%p A232189:= select(t -> Primes[t]-t mod 10^4=0, [$1..nops(Primes)]):

%p Primes[A232189]; # _Robert Israel_, Jul 02 2015

%t Select[Prime[Range[200000]],Mod[#,10000]==Mod[PrimePi[#],10000]&] (* _Harvey P. Dale_, Jul 16 2021 *)

%o (PARI) p=10007;n=1230;while(n<10^6,p=nextprime(p+1);n=n+1;if(p%10^4==n%10^4,print1(p, ", ")))

%o (MATLAB)

%o P = primes(10^7);

%o R = mod(P - [1:size(P,2)],10000);

%o A232189 = find(R==0);

%o P(A232189) % _Robert Israel_, Jul 02 2015

%o (PARI) n=0; forprime(p=2,1e7, if(Mod(n++,10000)==p, print1(p", "))) \\ _Charles R Greathouse IV_, Jul 05 2015

%Y Cf. A085598, A232102, A232104, A232189.

%K nonn,base,less

%O 1,1

%A _Antonio Roldán_, Nov 20 2013