A154553 - OEIS

%I #11 May 14 2013 11:45:04

%S 2,3,23,503,991,1381,1621,3301,4211,5471,5683,6563,6581,7351,7369,

%T 7829,8179,8849,10061,11299,11789,13841,14389,15823,16981,17839,18199,

%U 20563,21089,24151,24989,25321,25609,26203,28001,28403,28433,32003,35671

%N Lesser of two consecutive primes, p < q, such that both p*q+p-q and p*q-p+q are prime numbers.

%C 2*3-1=5;2*3+1=7, 3*5-2=13;3*5+2=17, ...

%H Paolo P. Lava, <a href="/A154553/b154553.txt">Table of n, a(n) for n = 1..200</a>

%p with(numtheory); A154553:=proc(q) local a,b,n;

%p for n from 42676 to q do a:=ithprime(n); b:=nextprime(a);

%p if isprime(a*b+a-b) and isprime(a*b-a+b) then print(a);

%p fi; od; end: A154553(10^9); # _Paolo P. Lava_, May 14 2013

%t lst={};Do[p=Prime[n];pn=Prime[n+1];d=pn-p;If[PrimeQ[p*pn-d]&&PrimeQ[p*pn+d],AppendTo[lst,p]],{n,8!}];lst

%t pnQ[{p_,q_}]:=And@@PrimeQ[{p*q+p-q,p*q-p+q}]; Transpose[Select[ Partition[ Prime[Range[4000]],2,1],pnQ]][[1]] (* _Harvey P. Dale_, Jul 12 2012 *)

%Y Cf. A138111, A138170, A154550, A154551, A154552

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 11 2009

%E Edited by _Omar E. Pol_, Jan 12 2009