A094105 - OEIS

%I #39 Jan 03 2025 05:43:38

%S 13,19,29,37,47,127,137,181,283,307,317,367,389,541,563,577,587,677,

%T 743,811,839,907,929,937,947,1031,1093,1283,1297,1453,1489,1567,1801,

%U 1847,1913,2027,2347,2381,2467,2477,2617,2647,2657,2729,2749,2777,2803,2819

%N Primes of the form prime(k) + 2*prime(k+1).

%C No intersection with A094104 (Primes of the form 2*prime(m)+prime(m+1)): an integer of the form 2*prime(m)+prime(m+1) cannot be of the form prime(n)+2*prime(n+1). - _Zak Seidov_, Feb 16 2012

%H Zak Seidov, <a href="/A094105/b094105.txt">Table of n, a(n) for n = 1..1001</a> [a(273), a(274) corrected by _Georg Fischer_, Jan 03 2025]

%e a(9) = 89 + 2*97 = 283.

%t f[n_] := (Prime[n] + 2Prime[n + 1]); f[ # ] & /@ Select[Range[160], PrimeQ[f[ # ]] &] (* _Robert G. Wilson v_, May 07 2004 *)

%t Select[#[[1]]+2*#[[2]]&/@Partition[Prime[Range[200]],2,1],PrimeQ] (* _Harvey P. Dale_, May 08 2015 *)

%t Select[Table[Prime[n] + 2 Prime[n + 1], {n, 200}], PrimeQ] (* _Vincenzo Librandi_, Jul 25 2015 *)

%o (PARI) q=2;forprime(p=3,1000,if(isprime(r=q+2*p),print1(r,","));q=p)

%o (Magma) [a: n in [1..200] | IsPrime(a) where a is NthPrime(n) + 2*NthPrime(n+1)]; // _Vincenzo Librandi_, Jul 25 2015

%Y Cf. A094104, A364411.

%K nonn,easy

%O 1,1

%A _Giovanni Teofilatto_, May 02 2004

%E Corrected and extended by _Klaus Brockhaus_ and _Robert G. Wilson v_, May 07 2004