A108156 Numbers n such that a(n) is prime, where a(n) = a(n-1) + a(n-2), a(1) = 3794765361567513, a(2) = 20615674205555510.

138, 163, 190, 523, 1855, 3228, 3579, 6468, 7170, 10230, 12783, 17259, 60139, 91315, 97923, 101823, 156075

Offset: 1

Author

Alonso del Arte, Jun 06 2005

Keywords

• nonn

Comments

In his biography of Paul Erdős, Hoffman cited Wilf's Fibonacci-like primefree sequence (A083216). But, as Weisstein points out, Hoffman inadvertently switched the two initial terms, resulting in a sequence that appears primefree for the first 137 terms. Term 138 is 439351292910452432574786963588089477522344721, which is prime. The first Mathematica program below comes from Weisstein's Mathematica notebook.

References

• Paul Hoffman. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, 1998.

Links

• Eric Weisstein's World of Mathematics, Primefree Sequence.
• Herbert S. Wilf, Letters to the Editor Math. Mag. 63, 284, 1990.

Crossrefs

Cf. A083216.

Programs

Mathematica

a[1] := 3794765361567513; a[2] := 20615674205555510; a[n_] := a[n] = a[n - 2] + a[n - 1]; Flatten[Position[Table[a[n], {n, 10^4}], ?PrimeQ]] (* _Eric W. Weisstein *)
Flatten[Position[LinearRecurrence[{1,1},{3794765361567513,20615674205555510},160000],?PrimeQ]] (* _Harvey P. Dale, Nov 29 2011 *)

Extensions

a(10)-a(12) from Robert G. Wilson v, Jun 07 2005

a(13) from Eric W. Weisstein, Sep 23 2005

a(14) from Eric W. Weisstein, Oct 06 2005

a(15)-a(16) from Eric W. Weisstein, Oct 10 2005

a(17) from Eric W. Weisstein, Nov 09 2005

Definition adapted to offset by Georg Fischer, Jun 18 2021