A138170 Prime numbers p1 such that p1*p2 + (p2 mod p1) is a prime, where p2 is the next prime after p1.

2, 3, 5, 23, 31, 61, 83, 89, 149, 179, 239, 251, 263, 269, 353, 367, 419, 433, 449, 503, 557, 569, 571, 587, 653, 701, 733, 761, 839, 941, 983, 991, 1109, 1123, 1187, 1193

Offset

1,1

Comments

Prime numbers p1 such that p1*p2+p2-p1 is a prime, where p2 is the next prime after p1. - J. M. Bergot and Robert Israel, Dec 30 2021

Links

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

Example

2 is prime, 3 is next prime, 2*3 + (3 mod 2) =  6 + 1 =  7;
3 is prime, 5 is next prime, 3*5 + (5 mod 3) = 15 + 2 = 17;
5 is prime, 7 is next prime, 5*7 + (7 mod 5) = 35 + 2 = 37.

Mathematica

a={}; Do[p1=Prime[n]; p2=Prime[n+1]; e=p1*p2+Mod[p2, p1]; If[PrimeQ[e], AppendTo[a, p1]], {n, 10^2*2}]; a
pnQ[n_]:=Module[{np=NextPrime[n]}, PrimeQ[n*np+Mod[np, n]]]; Select[Prime[ Range[200]], pnQ] (* Harvey P. Dale, Mar 09 2014 *)
Select[Partition[Prime[Range[200]], 2, 1], PrimeQ[Times@@#+Mod[#[[2]], #[[1]]]]&][[;; , 1]] (* Harvey P. Dale, Apr 06 2023 *)

Crossrefs

Sequence in context: A023231 A034470 A237812 * A105885 A228830 A339062

Adjacent sequences: A138167 A138168 A138169 * A138171 A138172 A138173

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 06 2008

Status

approved