OFFSET
2,1
COMMENTS
The definition is similar to that for A123159, but considering "p + n^x" and "p - n^x".
What does "conjectured" mean? A positive integer k is a candidate if:
1) gcd(k, n) = 1,
2) gcd(k^2-1, n-1) = 1,
3) every term in the sequence k + n^x is divisible by one of the prime numbers of a covering set,
4) all numbers of the form k - n^x are composite, k > n^x + 1, x >= 0.
The main problem is to prove that the given terms are indeed correct.
A quick search showed that a(8) = 47, a(14) = 11, a(20) = 13, a(27) = 512, a(29) = 26, a(32) = 23, a(34) = 99.
This is an interesting sequence: it leads to new classes of numbers. For example, the integer 30666137 is probably the smallest number that is simultaneously a Polignac number and a Sierpinski number.
CROSSREFS
KEYWORD
nonn
AUTHOR
Arkadiusz Wesolowski, Mar 12 2017
STATUS
approved