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

1,1

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)?

Links

Hal M. Switkay, Table of n, a(n) for n = 1..158

Example

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

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 *)

Crossrefs

Cf. A025487, A344385.

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

Sequence in context: A165671 A162855 A194954 * A299956 A368732 A192503

Adjacent sequences: A344381 A344382 A344383 * A344385 A344386 A344387

Keyword

nonn

Author

Hal M. Switkay, May 16 2021

Status

approved