A073662 - OEIS

%I #14 Feb 28 2019 03:18:29

%S 2,6,10,4,18,22,16,12,8,14,20,26,36,28,24,32,38,42,34,30,40,52,46,66,

%T 48,44,54,64,70,60,50,56,80,68,62,84,74,90,72,58,76,88,94,78,82,96,

%U 100,106,120,86,98,104,122,108,112,118,102,116,132,124,142,114,110,128,92

%N Rearrangement of even numbers such that a(k)*a(k+1) + 1 is a prime for all k.

%C a(1)=2; a(n) is the smallest number not already in the sequence such that a(n)*a(n-1) + 1 is a prime. Some numbers retain their places (that is an even number 2n retains its n-th position), such numbers are in A076023.

%H Robert Israel, <a href="/A073662/b073662.txt">Table of n, a(n) for n = 1..10000</a>

%p Avail:= 2*[$2..110]:

%p A[1]:= 2:

%p for n from 2 do

%p     found:= false:

%p     for i in Avail do

%p       if isprime(i*A[n-1]+1) then

%p         A[n]:= i;

%p         Avail:= subs(i=NULL,Avail);

%p         found:= true;

%p         break

%p      fi

%p     od;

%p     if not found then break fi

%p od:

%p seq(A[i],i=1..n-1); # _Robert Israel_, Jul 16 2018

%t amax = 200; a[1] = 2; aa = Range[4, amax, 2];

%t a[n_] := a[n] = For[k = 1, k <= Length[aa], k++, an = aa[[k]]; If[PrimeQ[ a[n - 1] an + 1], aa = Delete[aa, k]; Return[an]]];

%t DeleteCases[Array[a, Floor[amax/2]], Null] (* _Jean-François Alcover_, Feb 28 2019 *)

%Y Cf. A073661, A076023.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Aug 10 2002

%E More terms from _Hans Havermann_, Sep 23 2002