A347537 a(n) is the smallest prime p such that the polynomial k^4 + k^3 + k^2 + k + p yields primes for k = 0..n-1, but not for k = n.

2, 3, 13, 37, 109, 7, 1093, 457, 43, 430879, 130901527, 1838420599, 48181700197

Offset

1,1

Links

Table of n, a(n) for n=1..13.

Example

At k=0, k^4 + k^3 + k^2 + k + p is, of course, prime for every prime p.
a(1)=2 because 2 is the smallest prime p such that 1^4 + 1^3 + 1^2 + 1 + p = 4 + p is not prime: 4 + 2 = 6 = 2*3.
a(2)=3 because 3 is the smallest prime p such that k^4 + k^3 + k^2 + k + p is prime for k=1 but not for k=2, i.e., such that 4 + p is prime but 2^4 + 2^3 + 2^2 + 2 + p = 30 + p is not prime: 4 + 3 = 7 is prime but 30 + 3 = 33 = 3*11.
a(6)=7 because 7 is the smallest prime p such that k^4 + k^3 + k^2 + k + p is prime for k = 1..5, but not for k = 6: 4 + 7 = 11, 30 + 7 = 37, 120 + 7 = 127, 340 + 7 = 347, and 780 + 7 = 787, but 1554 + 7 = 1561 = 7*223.

Crossrefs

Cf. A247949, A247966, A248206, A253915.

Sequence in context: A082539 A168483 A100424 * A289549 A259261 A141511

Adjacent sequences: A347534 A347535 A347536 * A347538 A347539 A347540

Keyword

nonn,more

Author

Jon E. Schoenfield, Sep 11 2021

Extensions

a(13) from Jinyuan Wang, Sep 11 2021

Status

approved