A344776 - OEIS

%I #16 Jun 07 2021 18:51:01

%S 2,11,7,19,103,163,263,719,3119,3779,6719,18719,7559,67679,52919,

%T 181439,138599,241919,818999,262079,453599,665279,1542239,1713599,

%U 1330559,4979519,2741759,5569199,7197119,5745599

%N a(n) is the least prime p such that there are exactly n pairs of primes (q,r) with p > q > r such that q | r + p and r | q + p.

%e a(3) = 19 because there are 3 pairs (3,2), (7,2), (11,3) with

%e 3 | 2+19, 2 | 3+19, 7 | 2+19, 2 | 7+19, 11 | 3+19, 3 | 11+19.

%p M:= 10000: N:= ithprime(M): B:= Vector(N):

%p a:= 1:

%p do

%p   a:= nextprime(a);

%p   if a >= N then break fi;

%p   b:= a;

%p   do

%p     b:= nextprime(b);

%p     if b >= N then break fi;

%p     c0:= chrem([-a,-b],[b,a]);

%p     cs:= select(isprime, [seq(c0+i*a*b,i=ceil((b+2-c0)/(a*b)) .. floor((N-c0)/(a*b)))]);

%p     B[cs]:= B[cs]+~1;

%p   od:

%p od:

%p V:= Array(0..14):

%p for i from 2 to N do

%p   v:= A[i];

%p   if V[v] = 0 then V[v]:= i fi

%p od:

%p convert(V,list);

%o (PARI) count_pairs(n) = my(i=0); forprime(q=1, n-1, forprime(r=1, q-1, if((r+n)%q==0 && (q+n)%r==0, i++))); i

%o a(n) = forprime(p=1, , if(count_pairs(p)==n, return(p))) \\ _Felix Fröhlich_, May 28 2021

%Y Cf. A344788.

%K nonn,more

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, May 28 2021

%E a(15)-a(17) from _Chai Wah Wu_, Jun 04 2021

%E a(18) from _Bert Dobbelaere_, Jun 07 2021

%E a(19)-a(21) from _Chai Wah Wu_, Jun 04 2021

%E a(22)-a(29) from _Bert Dobbelaere_, Jun 07 2021