A344385 Numbers k of least prime signature (A025487) such that k-1 or k+1 is prime.

1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 72, 96, 128, 180, 192, 210, 240, 256, 360, 384, 420, 432, 480, 576, 720, 768, 840, 864, 1152, 1260, 1296, 1440, 1800, 2160, 2310, 2520, 2592, 2880, 3360, 3456, 4620, 5040, 5400, 6144, 6300, 6480, 6720, 6912, 7560

Offset: 1

Author

Hal M. Switkay, May 16 2021

Keywords

• nonn

Comments

The corresponding prime numbers are A344384.

64 is the first number of least prime signature not in this sequence.

Questions: 1) Is this sequence infinite? 2) Is log(a(n)) = O(log(n)^2)? For the first 132 terms, log(a(n)) is fit unusually well by a quadratic polynomial in log(n).

Examples

			16 is a term because 16 is in A025487 and 16 + 1 is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..132 from Hal M. Switkay)

Crossrefs

Cf. A000040, A025487, A344384.

Programs

Mathematica

(* Load the function f[n] at A025487, then: *)
Select[Union@ Flatten@ f[6], AnyTrue[# + {-1, 1}, PrimeQ] &]
(* or use the b-file at A025487: *)
Select[TakeWhile[Import["https://oeis.org/A025487/b025487.txt", "Data"], Length@ # == 2 &][[All, -1]], AnyTrue[# + {-1, 1}, PrimeQ] &] (* Michael De Vlieger, May 16 2021 *)