A073666 Rearrangement of natural numbers such that a(k)*a(k+1) + 1 is a prime for all k.

1, 2, 3, 4, 7, 6, 5, 8, 9, 12, 13, 10, 15, 14, 17, 18, 11, 30, 19, 22, 16, 21, 20, 23, 26, 33, 34, 27, 28, 24, 25, 42, 31, 36, 32, 29, 38, 39, 48, 37, 40, 43, 46, 51, 50, 45, 52, 49, 54, 44, 47, 56, 41, 62, 59, 60, 53, 66, 35, 68, 57, 58, 55, 70, 61, 76, 63, 74, 69, 72, 71, 98

Offset: 1

Author

Amarnath Murthy, Aug 10 2002

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A092842, A081942, A081943, A092829.

Cf. A073667.

Cf. A096100.

Programs

Mathematica

a[1]=1; a[n_]:=a[n]=(For[c=Sort[Table[a[k], {k, n-1}]]; d=Append[c, Last[c]+1]; m=First[Complement[Range[Last[d]], c]], MemberQ[c, m]||!PrimeQ[m*a[n-1]+1], m++ ]; m); Table[a[k], {k, 70}] (* Farideh Firoozbakht, Apr 14 2004 *)

PARI

A073666(n,show=1,a=1,u=[a])={for(n=2,n,show&&print1(a",");for(k=u[1]+1,9e9,!setsearch(u,k) && isprime(a*k+1) && (a=k) && break);u=setunion(u,[a]); while(#u>1&&u[2]==u[1]+1,u=u[2..-1]));a} \\ Use 2nd, 3rd or 4th optional arg to display intermediate terms, to use another starting value, to exclude some terms. - M. F. Hasler, Nov 24 2015

Extensions

More terms from Jason Earls, Aug 26 2002

Offset changed to 1 by Ivan Neretin, Mar 06 2016