A094383 Primes p such that d>0 exists and p-d, p-2*d and p-3*d are also primes.

23, 29, 41, 43, 53, 59, 79, 83, 97, 101, 103, 107, 113, 127, 131, 139, 149, 151, 157, 163, 167, 173, 181, 191, 193, 197, 199, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 313, 317, 331, 347, 349, 353, 359, 367, 373, 383

Offset

1,1

Comments

Conjecture: only 25 primes are not in the sequence, namely 2, 3, 5, 7, 11, 13, 17, 19, 31, 37, 47, 61, 67, 71, 73, 89, 109, 137, 179, 211, 277, 337, 379, 499, 557. - Alex Ratushnyak, Sep 08 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

59=prime(17) -> 59-6=53=prime(16) -> 53-6=47=prime(15) ->
47-6=41=prime(13), therefore 59 is a term; also 59 -> 59-18=41=prime(13) ->
41-18=23=prime(9) -> 23-18=5=prime(3).

Mathematica

prms = 3; fQ[p_] := Module[{d = 1}, While[prms*d < p && Union[PrimeQ[p - Range[prms]*d]] != {True}, d++]; prms*d < p]; Select[Prime[Range[2, PrimePi[383]]], fQ] (* T. D. Noe, Sep 08 2012 *)

Prog

(PARI) is(n)=my(t); forprime(p=2, n-6, if((n-p)%3==0 && isprime((t=(n-p)/3)+p) && isprime(2*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

Crossrefs

Cf. A094382, A216495, A216496, A216497, A216498, A216468.

Sequence in context: A173709 A225319 A228139 * A166565 A050207 A162658

Adjacent sequences: A094380 A094381 A094382 * A094384 A094385 A094386

Keyword

nonn

Author

Reinhard Zumkeller, Apr 28 2004

Status

approved