A108156 - OEIS

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

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OFFSET

1,1

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

Table of n, a(n) for n=1..17.

Eric Weisstein's World of Mathematics, Primefree Sequence.

Herbert S. Wilf, Letters to the Editor Math. Mag. 63, 284, 1990.

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 *)

CROSSREFS

Cf. A083216.

Sequence in context: A107939 A008888 A045045 * A264897 A202441 A187206

Adjacent sequences: A108153 A108154 A108155 * A108157 A108158 A108159

KEYWORD

nonn

AUTHOR

Alonso del Arte, Jun 06 2005

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

STATUS

approved