A261792 Primes of the form k*pi(k) - 1, where pi(k) is the number of primes <= k.

5, 7, 17, 31, 59, 83, 89, 151, 167, 233, 251, 373, 443, 467, 479, 601, 643, 719, 863, 911, 1019, 1097, 1151, 1187, 1291, 1439, 1553, 1637, 1759, 1931, 2207, 2861, 3023, 3389, 3449, 3539, 3659, 3719, 3779, 3967, 4759, 4793, 4861, 5471, 5507, 6269, 6551, 6959, 7039, 7079, 7643, 7727, 7853, 7937, 8623

Offset: 1

Author

Ilya Gutkovskiy, Sep 01 2015

Keywords

• nonn

Comments

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

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...

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime Number
• Eric Weisstein's World of Mathematics, Prime Counting Function

Crossrefs

Cf. A000040, A000720, A128913.

Programs

Mathematica

Select[Array[# PrimePi[#] - 1 &, {200}], PrimeQ] (* Michael De Vlieger, Sep 01 2015 *)

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

Extensions

Terms a(32)-a(55) added by Michael De Vlieger, Sep 01 2015

Corrected by Charles R Greathouse IV, Sep 18 2015