A216944 The least odd prime p for which the n-th prime can be written as 3p + q - 3 for some odd prime q.

3, 3, 3, 3, 3, 3, 5, 3, 5, 3, 3, 3, 3, 7, 3, 5, 3, 3, 5, 3, 7, 5, 3, 3, 3, 3, 7, 7, 3, 5, 5, 5, 3, 3, 7, 3, 3, 7, 5, 5, 3, 3, 5, 5, 11, 3, 3, 3, 5, 5, 3, 3, 3, 11, 3, 5, 3, 5, 11, 7, 3, 3, 7, 3, 11, 5, 3, 3, 7, 3, 3, 11, 3, 7, 5, 5, 7, 5, 5, 5, 3, 5, 3, 7, 5, 3, 3

Offset

5,1

Comments

Conjecture: Any prime >= 11 can be written this way.

Links

Robert Israel, Table of n, a(n) for n = 5..10000

Example

The corresponding q and prime(n): (5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (19,31), (31,37), (29,41), (37,43), (41,47), (47,53), (53,59), (43,61), (61,67), (67,73), (73,79), (71,83), (83,89), (79,97), (89,101), (97,103), (101,107), (103,109), (107,113), (109,127), (113,131), (131,137), (127,139), (137,149), (139,151), (151,157), (157,163), (149,167), (167,173), (173,179), (163,181), (179,191), (181,193), (191,197), (193,199), (199,211), (211,223), (197,227), (223,229), (227,233), (233,239), (229,241), (239,251), (251,257), (257,263), (263,269), (241,271),  (271,277), (269,281), (277,283), (281,293), (277,307), (293,311), (307,313), (311,317), (313,331), (331,337), (317,347), (337,349), (347,353), (353,359), (349,367), (367,373), (373,379), (353,383), (383,389), (379,397), (389,401), (397,409), (401,419), (409,421), (419,431), (421,433), (433,439), (431,443), (443,449), (439,457), (449,461), (457,463), (461,467), (467,479).

Maple

f:= proc(n) local p, q;
  p:= 2;
  while 3*p<n+3 do
    p:= nextprime(p);
    if isprime(n-3*p+3) then return p fi;
  od;
FAIL
end proc:
p:= 7: Res:= NULL:
for i from 1 to 100 do
p:= nextprime(p); Res:= Res, f(p);
od:
Res; # Robert Israel, Mar 08 2018

Prog

(PARI) a(n)=my(r=prime(n)+3); forprime(p=3, r\3-1, if(isprime(r-3*p), return(p))) \\ Charles R Greathouse IV, Dec 07 2014

Crossrefs

Sequence in context: A210509 A362049 A333819 * A178832 A111233 A210746

Adjacent sequences: A216941 A216942 A216943 * A216945 A216946 A216947

Keyword

nonn

Author

Marius Coman, Sep 20 2012

Extensions

New name from Charles R Greathouse IV, Dec 07 2014

Corrected by Charles R Greathouse IV, Dec 07 2014

Status

approved