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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 29 17:01 EDT 2020. Contains 337432 sequences. (Running on oeis4.)