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(PARI) n=0; m=1; for(k=0, 10^8, my(j=k^2+k+41); if(isprime(j), n++); if(k>==m, m=m*10; print1(n, ", ")))
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.
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, ...
allocated Number of primes of the form P(k)=k^2 + k + 41 for Hugo Pfoertnerk <= 10^n, where P(k) is Euler's prime-generating polynomial A202018.
2, 11, 87, 582, 4149, 31985, 261081, 2208197, 19132653
0,1
(PARI) n=0; m=1; for(k=0, 10^8, my(j=k^2+k+41); if(isprime(j), n++); if(k>=m, m=m*10; print1(n, ", ")))
allocated
nonn,more
Hugo Pfoertner, Jan 30 2020
approved
editing
allocating
allocated
allocated for Hugo Pfoertner
allocating
approved