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Primes of the form k*pi(k) - 1, where pi(k) is the number of primes <= k.
1

%I #24 Mar 08 2023 05:27:02

%S 5,7,17,31,59,83,89,151,167,233,251,373,443,467,479,601,643,719,863,

%T 911,1019,1097,1151,1187,1291,1439,1553,1637,1759,1931,2207,2861,3023,

%U 3389,3449,3539,3659,3719,3779,3967,4759,4793,4861,5471,5507,6269,6551,6959,7039,7079,7643,7727,7853,7937,8623

%N Primes of the form k*pi(k) - 1, where pi(k) is the number of primes <= k.

%C Sequence elements A000040 of the form A128913(n) - 1.

%C Primes of the form pi(k)*pi(prime(k)) + e^(i*Pi), where pi(k) is the number of primes <= k, i is the imaginary unit, Pi = 3.14159...

%H Charles R Greathouse IV, <a href="/A261792/b261792.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeNumber.html">Prime Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function</a>

%t Select[Array[# PrimePi[#] - 1 &, {200}], PrimeQ] (* _Michael De Vlieger_, Sep 01 2015 *)

%o (PARI) list(lim)=my(v=List(),k,pi,t); while(1, if(isprime(k++), pi++); t=k*pi-1; if(t>lim, return(Vec(v))); if(isprime(t), listput(v,t))) \\ _Charles R Greathouse IV_, Sep 18 2015

%Y Cf. A000040, A000720, A128913.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Sep 01 2015

%E Terms a(32)-a(55) added by _Michael De Vlieger_, Sep 01 2015

%E Corrected by _Charles R Greathouse IV_, Sep 18 2015