A258187 Numbers m such that either m^k - 1 or m^k - 2 is prime for some positive k, but not both.

3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 62, 63, 65, 67, 68, 69, 71, 72, 73, 74, 75, 77, 79, 80, 81, 83, 84, 85, 87, 89, 90, 91, 93, 95, 97, 98, 99, 101

Offset

1,1

Comments

From R. J. Mathar, Jul 22 2015: (Start)

10 is not in the sequence because 10^k-2 is even and 10^k-1 is divisible by 3 (because 10^k mod 3 = 1 as 10 mod 3 = 1). 16 is not in the sequence because 16^k-2 is even and 16^k-1 is divisible by 3 (because 16^k mod 3 = 1 as 16 mod 3 = 1). For the same reason almost all even numbers of the form 3m+1 (A016957) are absent, the only exception being 4, as 4^1-1 is a prime.

36 is not in the sequence because 36^k-1 is even and 36^k-1 is divisible by 5 (because 36^k mod 5 = 1 as 36 mod 5 = 1). This reasoning excludes all terms of A017341 (except for 6, as 6^1-1 is prime) from this sequence. With the same methology we can fish for (and exclude) even numbers of the form m*p+1 for primes p >= 3. (End)

Links

Table of n, a(n) for n=1..74.

Example

2 is not in this sequence because 2^2 - 1 = 3 and 2^2 - 2 = 2 are both prime.
3 is in this sequence because 3^1 - 1 = 2 (prime) and 3^1 - 2 = 1 (nonprime) or 3^2 - 1 = 5 (prime) and 3^2 - 2 = 4 (nonprime).

Prog

(PARI) is(n)=n>2 && if(n%2, 1, isprime(n-1)) \\ Charles R Greathouse IV, Jun 03 2015

Crossrefs

Cf. A016957, A017341.

Sequence in context: A304806 A304810 A026469 * A039237 A039181 A298111

Adjacent sequences: A258184 A258185 A258186 * A258188 A258189 A258190

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, May 23 2015

Status

approved