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

%I #34 Dec 14 2019 21:28:57

%S 1,5,11,11,17,17,41,41,41,41,41,41,19421,19421,333491,601037,601037,

%T 5237651,9063641,12899891,24073871,24073871,28537121,67374467,

%U 67374467,67374467,67374467,146452961,13236860171,13236860171,17959429571,57391479317,57391479317

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

%C 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.

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

%H William P. Orrick, <a href="/A181667/b181667.txt">Table of n, a(n) for n = 1..59</a>

%H M. J. Jacobson, Jr., <a href="http://pages.cpsc.ucalgary.ca/~jacobs/PDF/mthesis.pdf">Master's Thesis</a>, University of Manitoba, 1995. (See Table 6.6, which lists values of 4a(n)-1.)

%e 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.

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

%K nonn

%O 1,2

%A _Esteban Crespi de Valldaura_, Feb 04 2011

%E a(29) corrected and more terms added by _William P. Orrick_, Mar 17 2017