A346147 Primes p such that p*p' mod (p+p') and floor(p*p'/(p+p')) are prime, where p' is the next prime after p.

5, 11, 13, 113, 139, 157, 179, 193, 313, 359, 479, 509, 691, 773, 919, 953, 1019, 1039, 1093, 1453, 1571, 1873, 2297, 2341, 2357, 2459, 2633, 3089, 3229, 3253, 3571, 4021, 4219, 4483, 4523, 4663, 4889, 4933, 4943, 5113, 5153, 5179, 5233, 5261, 5323, 5449, 5591, 5639, 6037, 6073, 6079, 6337, 6373

Offset

1,1

Comments

Primes prime(k) such that A212769(k) and A160830(k) are both prime.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 13 is a term because 13 and 17 are consecutive primes with (13*17) mod (13+17) = 11 and floor(13*17/(13+17)) = 7 are prime.

Maple

P:= select(isprime, [2, seq(i, i=3..10^5, 2)]):
f:= proc(n) local s, t;
   s:= P[n]+P[n+1];
   t:= P[n]*P[n+1];
   if isprime(t mod s) and isprime(floor(t/s)) then return P[n] fi
end proc:
map(f, [$1..nops(P)-1]);

Mathematica

Select[Partition[Select[Range[6400], PrimeQ], 2, 1], PrimeQ[Mod[(p = First[#] * Last[#]), (s = First[#] + Last[#])]] && PrimeQ[Quotient[p, s]] &][[;; , 1]] (* Amiram Eldar, Jul 06 2021 *)

Prog

(PARI) list(lim)=my(v=List(), p=2, pq); forprime(q=3, nextprime(lim\1+1/2), pq=p*q; if(isprime(pq%(p+q)) && isprime(pq\(p+q)), listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 06 2021
(Python)
from sympy import nextprime, isprime
p, q, A346147_list = 2, 3, []
while len(A346147_list) < 1000:
    if isprime(p*q % (p+q)) and isprime(p*q//(p+q)):
        A346147_list.append(p)
    p, q = q, nextprime(q) # Chai Wah Wu, Jul 06 2021

Crossrefs

Cf. A160830, A212769.

Sequence in context: A352534 A236411 A073615 * A275118 A275640 A275805

Adjacent sequences: A346144 A346145 A346146 * A346148 A346149 A346150

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 06 2021

Status

approved