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

Author

Juri-Stepan Gerasimov, May 23 2015

Keywords

• nonn
• easy

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)

Examples

			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).
		

Crossrefs

Cf. A016957, A017341.

Programs

PARI

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