

A187868


Primes of the form 100^k  10^k + 1.


1




OFFSET

1,1


COMMENTS

These primes correspond to k = 2, 4, 6, and 8. There are no other primes of this form for k up to 10000. These primes appear in A187614 because the decimal representation of their reciprocal contains only the digits 0, 1, 8, and 9.
Because these numbers are values of the sixth cyclotomic polynomial, by Theorem 1 of Golomb, the only k that can produce primes are the 3smooth numbers, 2^i*3^j (A003586).
Next term has k > 1000000.  Robert Gelhar, Aug 20 2020


REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 85.


LINKS

Table of n, a(n) for n=1..4.
Solomon W. Golomb, Cyclotomic polynomials and factorization theorems, Amer. Math. Monthly 85 (1978), 734737.


MATHEMATICA

Select[Table[100^n  10^n + 1, {n, 1000}], PrimeQ]


CROSSREFS

Cf. A003586, A168624, A187614.
Sequence in context: A237917 A205612 A205350 * A072848 A145381 A212401
Adjacent sequences: A187865 A187866 A187867 * A187869 A187870 A187871


KEYWORD

nonn,more


AUTHOR

T. D. Noe, Mar 14 2011


STATUS

approved



