OFFSET
1,1
COMMENTS
There exist infinitely many such prime numbers, as proved by @GH from MO in the link provided to Mathoverflow. - Juan Moreno Borrallo, Mar 15 2021
It follows that the sum of prime numbers up to the square root of n is infinitely often equal to the prime counting function up to n. - Juan Moreno Borrallo, Mar 15 2021
LINKS
Juan Moreno Borrallo, An Approximation to the Prime Counting Function Through the Sum of Consecutive Prime Numbers, viXra:1710.0205, 2017.
Juan Moreno Borrallo, The prime counting function and the sum of prime numbers, viXra:1911.0316, 2019.
EXAMPLE
The square root of the 5th prime (11) is 3, and the sum of prime numbers up to 3 is 2+3 = 5, so 11 is a term of the sequence.
MATHEMATICA
Select[Prime@ Range@ PrimePi[10^6], Total@ Prime@ Range@ PrimePi@ Sqrt[#] == PrimePi@ # &] (* Michael De Vlieger, Dec 27 2019 *)
PROG
(PARI) isok(p) = isprime(p) && (primepi(p) == sum(k=1, sqrtint(p), if (isprime(k), k))); \\ Michel Marcus, Nov 13 2019
(Magma) [NthPrime(k):k in [1..100000]| &+PrimesInInterval(1, Floor(Sqrt(NthPrime(k)))) eq k]; // Marius A. Burtea, Nov 13 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Juan Moreno Borrallo, Nov 13 2019
STATUS
approved