A059456 Unsafe primes: primes not in A005385.

2, 3, 13, 17, 19, 29, 31, 37, 41, 43, 53, 61, 67, 71, 73, 79, 89, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 173, 181, 191, 193, 197, 199, 211, 223, 229, 233, 239, 241, 251, 257, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337

Offset

1,1

Comments

A010051(a(n))*(1-A156659(a(n))) = 1; subsequence of A156657. - Reinhard Zumkeller, Feb 18 2009

Also, primes p such that p-1 is a non-semiprime. - Juri-Stepan Gerasimov, Apr 28 2010

Conjecture: From the sequence of prime numbers, let 2 and remove the first data iteration of 2*p+1; leave 3 and remove the prime data by the iteration 2*p+1 and we get the sequence. Example for p=2, remove(5,11,23,47); p=3, remove(7); p=13, p=17, p=19, p=23, remove(47); and so on. - Vincenzo Librandi, Aug 07 2010

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Dec 29 2024

Example

31 is here because (31-1)/2=15 is not prime. 2 and 3 are here because 1/2 and 1 are not prime numbers.

Mathematica

Complement[Prime@ Range@ PrimePi@ Max@ #, #] &@ Select[Prime@ Range@ 90, PrimeQ[(# - 1)/2] &] (* Michael De Vlieger, May 01 2016 *)
Select[Prime[Range[100]], PrimeOmega[#-1]!=2&] (* Harvey P. Dale, May 13 2018 *)

Prog

(PARI) is(n)=isprime(n) && !isprime(n\2) \\ Charles R Greathouse IV, May 02 2016

Crossrefs

Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330.

Initial terms for groups in A075712.

Sequence in context: A299543 A059670 A038975 * A274589 A019394 A048704

Adjacent sequences: A059453 A059454 A059455 * A059457 A059458 A059459

Keyword

nonn

Author

Labos Elemer, Feb 02 2001

Status

approved