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

3, 4, 6, 7, 8, 10, 12, 14, 15, 18, 19, 20, 21, 24, 25, 26, 29, 32, 34, 35, 49, 50, 54, 57, 59, 60, 62, 72, 77, 79, 87, 89, 94, 101, 104, 111, 115, 132, 134, 137, 138, 140, 141, 142, 148, 154, 161, 162, 164, 167, 168, 180, 181, 182, 183, 186, 190, 192, 195, 203, 204

Offset: 1

Author

Zak Seidov, May 02 2005

Keywords

• nonn

Comments

Or, numbers k such that A152117(k) is prime. - Zak Seidov, Feb 05 2016

Examples

			4*prime(4)+5*prime(5) = 4*7+5*11 = 83 prime.
		

Crossrefs

Cf. A152117, A119487.

Programs

Magma

[n: n in [1..250] | IsPrime(n*NthPrime(n)+(n+1)*NthPrime(n+1))]; // Vincenzo Librandi, Feb 06 2016

Mathematica

bb={};Do[If[PrimeQ[n Prime[n]+(n+1)Prime[n+1]], bb=Append[bb, n]], {n, 400}];bb
Select[Range[250],PrimeQ[# Prime[#]+(#+1)Prime[#+1]]&] (* Harvey P. Dale, Dec 08 2011 *)

PARI

isok(n) = isprime(n*prime(n)+(n+1)*prime(n+1)); \\ Michel Marcus, Feb 05 2016

PARI

lista(nn) = {for(n=1, nn, if(ispseudoprime(n*prime(n)+(n+1)*prime(n+1)), print1(n, ", ")));} \\ Altug Alkan, Feb 05 2016