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A248031 Least number k such that k^n +- k +- 1 is prime for all four possibilities, or 0 if no such k exists. 0
3, 15, 6, 0, 30594, 246819, 0, 4033590, 2298429, 0, 19209840, 13542816, 0, 3979836, 75524874, 0, 143635866, 220808901, 0, 14557221, 185958081, 0, 180438825, 320588085, 0, 499478574, 29105421, 0, 37340766, 1169275746, 0, 2051928486, 27069021, 0, 971311320 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(19) > 155*10^6.

For n == 2 (mod 3), k^n + k + 1 is divisible by k^2 + k + 1. Thus, for n > 2, if n == 2 (mod 3), a(n) = 0.

LINKS

Table of n, a(n) for n=2..36.

PROG

(PARI)

a(n)=if(n>2&&n==Mod(2, 3), return(0)); k=1; while(!ispseudoprime(k^n+k+1)||!ispseudoprime(k^n+k-1)||!ispseudoprime(k^n-k+1)||!ispseudoprime(k^n-k-1), k++); k

n=2; while(n<100, print1(a(n), ", "); n++)

CROSSREFS

Cf. A236056, A236764, A236766.

Sequence in context: A212203 A286783 A012881 * A066832 A102777 A102531

Adjacent sequences:  A248028 A248029 A248030 * A248032 A248033 A248034

KEYWORD

nonn

AUTHOR

Derek Orr, Oct 03 2014

EXTENSIONS

a(19)-a(27) from Jon E. Schoenfield, Oct 19 2014

a(28)-a(36) from Jon E. Schoenfield, Oct 22 2014

STATUS

approved

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Last modified October 18 23:44 EDT 2021. Contains 348071 sequences. (Running on oeis4.)