A172095 Integers k such that k-1,k,k+1 have few distinct primes: k=p^r, p odd prime, and (k^2-1)/8 divisible by at most two distinct prime factors.

3, 5, 7, 9, 11, 13, 17, 19, 27, 37, 53, 107, 163, 243, 2187, 2917, 4373, 8747, 1594323, 86093443

Offset: 1

Author

Dino Lorenzini (lorenzin(AT)uga.edu), Jan 25 2010

Keywords

• nonn
• hard
• more
• changed

Comments

Note the terms 3^1=3, 3^2=9, 3^3=27, 3^5=243, 3^7=2187, and 3^13=1594323. The other listed terms are prime.

Next term > 2^2000. - Max Alekseyev, Feb 16 2011

Crossrefs

Cf. A075081, A062547, A111974, A005105

Extensions

Edited and missing terms 3, 5, 9, 17 added by Max Alekseyev, Feb 16 2011