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A331876 revision #14

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

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, ...

PROG

(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, ", ")))

CROSSREFS

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

Sequence in context: A370475 A153304 A240998 * A305537 A036076 A372842

Adjacent sequences: A331873 A331874 A331875 * A331877 A331878 A331879

KEYWORD

nonn,more

AUTHOR

Hugo Pfoertner, Jan 30 2020

STATUS

proposed