

A073662


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


6



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
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OFFSET

1,1


COMMENTS

a(1)=2; a(n) is the smallest number not already in the sequence such that a(n)*a(n1) + 1 is a prime. Some numbers retain their places (that is an even number 2n retains its nth 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[n1]+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..n1); # 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] (* JeanFrançois Alcover, Feb 28 2019 *)


CROSSREFS

Cf. A073661, A076023.
Sequence in context: A220338 A052194 A320383 * A086553 A004055 A077933
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



