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A138170 Prime numbers p1 such that p1*p2 + (p2 mod p1) is a prime, where p2 is the next prime after p1. 6
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 19 03:20 EDT 2024. Contains 372666 sequences. (Running on oeis4.)