

A108156


Numbers n such that a(n) is prime, where a(n) = a(n1) + a(n2), a(1) = 3794765361567513, a(2) = 20615674205555510.


0



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 Fibonaccilike 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



