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

1,1

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

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 *)

Crossrefs

Cf. A073661, A076023.

Sequence in context: A220338 A052194 A320383 * A086553 A342068 A004055

Adjacent sequences: A073659 A073660 A073661 * A073663 A073664 A073665

Keyword

nonn

Author

Amarnath Murthy, Aug 10 2002

Extensions

More terms from Hans Havermann, Sep 23 2002

Status

approved