|
%I #12 Jun 29 2021 17:10:26
%S 2,5,5,5,67,5,7,19,107,61,67,7,5,103,263,13,83,197,17,1097,709,103,
%T 2731,367,271,353,1951,43,1109,113,457,131,67,197,1427,199,379,7,1901,
%U 367,3889,8387,97,367,2297,613,89,6263,2017,127,2647,911,8831,45949,4051,2671,2927,883,4423,4027,11
%N a(n) is the first prime p such that p*2^n+q*3^n and p*3^n+q*2^n are both prime, where q is the prime following p.
%H Robert Israel, <a href="/A340777/b340777.txt">Table of n, a(n) for n = 0..1337</a>
%e a(3) = 5 because 5*2^3+7*3^3 = 229 and 5*3^n+7*2^n = 191 are prime.
%p f:= proc(n) local p,q;
%p q:= 2;
%p do
%p p:= q; q:= nextprime(q);
%p until isprime(p*2^n+q*3^n) and isprime(p*3^n + q*2^n);
%p p
%p end proc:
%p map(f, [$0..100]);
%t fpp[n_]:=Module[{p=2},While[!PrimeQ[p 2^n+NextPrime[p]3^n]|| !PrimeQ[p 3^n+ NextPrime[ p]2^n],p=NextPrime[p]];p]; Array[fpp,70,0] (* _Harvey P. Dale_, Jun 29 2021 *)
%o (PARI) a(n) = my(p=2, q=nextprime(p+1)); while(! (isprime(p*2^n+q*3^n) && isprime(p*3^n + q*2^n)), p=q; q=nextprime(p+1)); p; \\ _Michel Marcus_, Jan 21 2021
%Y Cf. A340694.
%K nonn
%O 0,1
%A _J. M. Bergot_ and _Robert Israel_, Jan 21 2021
|
