A331876 Number of primes of the form P(k) = k^2 + k + 41 for k <= 10^n, where P(k) is Euler's prime-generating polynomial A202018.

2, 11, 87, 582, 4149, 31985, 261081, 2208197, 19132653, 168806741, 1510676803

Offset: 0

Author

Hugo Pfoertner, Jan 30 2020

Keywords

• nonn
• more

Examples

			a(0) = 2 because 41 and 43 are the 2 primes generated for k <= 1 = 10^0.
a(1) = 11 because 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151 are the 11 primes generated for k <= 10^1, (A202018(10) = 151).
a(3) = 87 because 87 terms of A202018(0..100) are prime. The 14 composites occur for k = A007634(1..14): 40, 41, 44, 49, 56, ...
		

Crossrefs

Cf. A005846, A007634, A202018, A319906, A331877.

Programs

PARI

n=0;m=1;for(k=0,10^7,my(j=k^2+k+41);if(isprime(j),n++);if(k==m,m*=10;print1(n,", ")))