A344384 - OEIS

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

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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

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

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 A372629 A368732

Adjacent sequences: A344381 A344382 A344383 * A344385 A344386 A344387

KEYWORD

nonn

AUTHOR

Hal M. Switkay, May 16 2021

STATUS

approved