cp's OEIS Frontend

A105454 Numbers k such that k*prime(k)+(k+1)*prime(k+1) is prime.

%I A105454 #27 Aug 01 2025 19:25:50
%S A105454 3,4,6,7,8,10,12,14,15,18,19,20,21,24,25,26,29,32,34,35,49,50,54,57,
%T A105454 59,60,62,72,77,79,87,89,94,101,104,111,115,132,134,137,138,140,141,
%U A105454 142,148,154,161,162,164,167,168,180,181,182,183,186,190,192,195,203,204
%N A105454 Numbers k such that k*prime(k)+(k+1)*prime(k+1) is prime.
%C A105454 Or, numbers k such that A152117(k) is prime. - _Zak Seidov_, Feb 05 2016
%e A105454 4*prime(4)+5*prime(5) = 4*7+5*11 = 83 prime.
%t A105454 bb={};Do[If[PrimeQ[n Prime[n]+(n+1)Prime[n+1]], bb=Append[bb, n]], {n, 400}];bb
%t A105454 Select[Range[250],PrimeQ[# Prime[#]+(#+1)Prime[#+1]]&] (* _Harvey P. Dale_, Dec 08 2011 *)
%o A105454 (PARI) isok(n) = isprime(n*prime(n)+(n+1)*prime(n+1)); \\ _Michel Marcus_, Feb 05 2016
%o A105454 (PARI) lista(nn) = {for(n=1, nn, if(ispseudoprime(n*prime(n)+(n+1)*prime(n+1)), print1(n, ", ")));} \\ _Altug Alkan_, Feb 05 2016
%o A105454 (Magma) [n: n in [1..250] | IsPrime(n*NthPrime(n)+(n+1)*NthPrime(n+1))]; // _Vincenzo Librandi_, Feb 06 2016
%Y A105454 Cf. A152117, A119487.
%K A105454 nonn
%O A105454 1,1
%A A105454 _Zak Seidov_, May 02 2005