A073662 Rearrangement of even numbers such that a(k)*a(k+1) + 1 is a prime for all k.

2, 6, 10, 4, 18, 22, 16, 12, 8, 14, 20, 26, 36, 28, 24, 32, 38, 42, 34, 30, 40, 52, 46, 66, 48, 44, 54, 64, 70, 60, 50, 56, 80, 68, 62, 84, 74, 90, 72, 58, 76, 88, 94, 78, 82, 96, 100, 106, 120, 86, 98, 104, 122, 108, 112, 118, 102, 116, 132, 124, 142, 114, 110, 128, 92

Offset: 1

Author

Amarnath Murthy, Aug 10 2002

Keywords

• nonn

Comments

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.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073661, A076023.

Programs

Maple

Avail:= 2*[$2..110]:
A[1]:= 2:
for n from 2 do
    found:= false:
    for i in Avail do
      if isprime(i*A[n-1]+1) then
        A[n]:= i;
        Avail:= subs(i=NULL,Avail);
        found:= true;
        break
     fi
    od;
    if not found then break fi
od:
seq(A[i],i=1..n-1); # Robert Israel, Jul 16 2018

Mathematica

amax = 200; a[1] = 2; aa = Range[4, amax, 2];
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]]];
DeleteCases[Array[a, Floor[amax/2]], Null] (* Jean-François Alcover, Feb 28 2019 *)

Extensions

More terms from Hans Havermann, Sep 23 2002