A181667 Least integer m > 0 such that none of the first n primes divides any value of the polynomial x^2 + x + m.

1, 5, 11, 11, 17, 17, 41, 41, 41, 41, 41, 41, 19421, 19421, 333491, 601037, 601037, 5237651, 9063641, 12899891, 24073871, 24073871, 28537121, 67374467, 67374467, 67374467, 67374467, 146452961, 13236860171, 13236860171, 17959429571, 57391479317, 57391479317

Offset

1,2

Comments

All the elements of this sequence with n > 2 are congruent mod 30 to one of the polynomials x^2 + x + 11 or x^2 + x + 17.

The elements of the sequence have been taken from A060392, see below.

Links

William P. Orrick, Table of n, a(n) for n = 1..59

M. J. Jacobson, Jr., Master's Thesis, University of Manitoba, 1995. (See Table 6.6, which lists values of 4a(n)-1.)

Example

x^2 + x + 11 takes the values 11, 13, 17, 23, 31, 41, 53, 67, 83, ... never divisible by any of the primes 2, 3, or 5.

Crossrefs

a(n) equals min_{k > n} A060392(k).

Sequence in context: A205673 A245098 A352443 * A060846 A352354 A113002

Adjacent sequences: A181664 A181665 A181666 * A181668 A181669 A181670

Keyword

nonn

Author

Esteban Crespi de Valldaura, Feb 04 2011

Extensions

a(29) corrected and more terms added by William P. Orrick, Mar 17 2017

Status

approved