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

1,2

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A092842, A081942, A081943, A092829.

Cf. A073667.

Cf. A096100.

Sequence in context: A264966 A308728 A201543 * A092842 A343600 A343601

Adjacent sequences: A073663 A073664 A073665 * A073667 A073668 A073669

Keyword

nonn

Author

Amarnath Murthy, Aug 10 2002

Extensions

More terms from Jason Earls, Aug 26 2002

Offset changed to 1 by Ivan Neretin, Mar 06 2016

Status

approved