A344384 Prime numbers p such that p-1 or p+1 is a number of least prime signature (A025487).

2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 47, 59, 61, 71, 73, 97, 127, 179, 181, 191, 193, 211, 239, 241, 257, 359, 383, 419, 421, 431, 433, 479, 577, 719, 769, 839, 863, 1151, 1153, 1259, 1297, 1439, 1801, 2161, 2309, 2311, 2521, 2591, 2593, 2879, 3359, 3361

Offset: 1

Author

Hal M. Switkay, May 16 2021

Keywords

• nonn

Comments

The corresponding numbers of least prime signature are A344385.

19 is the first prime not in this sequence.

This sequence unites many familiar sequences of primes, including Fermat primes (A019434), Mersenne primes (A000668), primorial primes (A018239 and A057705), factorial primes (A088054), A007505, and A039687.

Questions: 1) Is this sequence infinite? 2) Is log(a(n)) = O(log(n)^2)?

Examples

			17 is a term because 17 - 1 = 16 is a number of least prime signature.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..158 from Hal M. Switkay)

Crossrefs

Cf. A025487, A344385.

Cf. A000668, A007505, A018239, A019434, A039687, A057705, A088054.

Programs

Mathematica

{2}~Join~Select[Prime@ Range[2, 900], AnyTrue[# + {-1, 1}, Times @@ MapIndexed[Prime[First[#2]]^#1 &, Sort[FactorInteger[#][[All, -1]], Greater] ] == # &] &] (* Michael De Vlieger, May 16 2021 *)