

A100891


Prime Padovan numbers.


1



2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 1558877695141608507751098941899265975115403618621811951868598809164180630185566719
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OFFSET

1,1


COMMENTS

Next term corresponds to Padovan(1262) and has 154 decimal digits.


REFERENCES

Midhat J. Gazale, "Gnomon: From Pharaohs to Fractals", Princeton University Press, 1999.


LINKS

Table of n, a(n) for n=1..12.
Ian Stewart, Tales of a Neglected Number.
Eric Weisstein's World of Mathematics, Padovan Sequence
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1).


FORMULA

a[0]=a[1]=a[2]=1; a[3]=a[4]=2; a[n]=a[n2]+a[n3]; a[n] is prime.


MAPLE

{ u=v=w=1; x=2; for (k=1, 1000, y = v+w; u = v; v = w; w = x; x = y; if (isprime(y), print(k " " y), ); ) }


MATHEMATICA

a[0] = 1; a[1] = a[2] = 0; a[n_] := a[n] = a[n  2] + a[n  3]; a /@ Select[ Range[1000], PrimeQ[ a[ # ]] &] (* Robert G. Wilson v, Jan 14 2005 *)
Rest[Select[LinearRecurrence[{0, 1, 1}, {1, 1, 2}, 1000], PrimeQ]] (* Harvey P. Dale, Mar 31 2012 *)


CROSSREFS

Cf. A000931.
Indices of prime Padovan numbers are A112882.
Sequence in context: A117639 A202263 A153014 * A051857 A050654 A215157
Adjacent sequences: A100888 A100889 A100890 * A100892 A100893 A100894


KEYWORD

nonn


AUTHOR

John Lien, Jan 10 2005


EXTENSIONS

More terms from Robert G. Wilson v, Jan 14 2005


STATUS

approved



