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A100891 Prime Padovan numbers. 1
2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 1558877695141608507751098941899265975115403618621811951868598809164180630185566719 (list; graph; refs; listen; history; text; internal format)
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[n-2]+a[n-3]; 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

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Last modified August 29 05:24 EDT 2015. Contains 261185 sequences.