A105399 Largest prime <= numbers of the form 6k+3 (duplicates removed).

3, 7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 67, 73, 79, 83, 89, 97, 103, 109, 113, 127, 131, 139, 151, 157, 163, 167, 173, 181, 193, 199, 211, 223, 229, 233, 241, 251, 257, 263, 271, 277, 283, 293, 307, 313, 317, 331, 337, 349, 353, 359, 367, 373, 379, 383, 389

Offset: 1

Author

Giovanni Teofilatto, May 01 2005

Keywords

• easy
• nonn

Comments

Apart from the initial 3, the same as A049591. [Proof from T. Khovanova, Jan 23 2008: True for primes up to 5 by inspection. Higher primes must be of the form 6k+1 or 6k+5 since 6k+2 and 6k+4 are divisible by 2 and 6k+3 is divisible by 3. So searching the prime p backwards from the composite, odd 6k+3 in steps of 2 implies that p+2, skipped during that scan, is composite. So p is not in A001359 but in A049591.] - R. J. Mathar, Jan 28 2008

Examples

			7 is in the sequence because 7 is the largest prime < 9=6*1+3.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A106002.

Cf. A049591.

Programs

Mathematica

pp[n_] := Block[{k = n},While[ ! PrimeQ[k], k-- ];k];Union[Table[pp[6n + 3], {n, 0, 65}]] (* Ray Chandler, Oct 17 2006 *)
Union[If[PrimeQ[#],#,NextPrime[#,-1]]&/@(6*Range[0,70]+3)] (* Harvey P. Dale, Aug 20 2021 *)

Extensions

Edited, corrected and extended by Ray Chandler, Oct 17 2006