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A005042 Primes formed by the initial digits of the decimal expansion of Pi.
(Formerly M3129)
28
3, 31, 314159, 31415926535897932384626433832795028841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The next term consists of the first 16208 digits of Pi and is too large to show here (see A060421). Ed T. Prothro found this probable prime in 2001.

A naive probabilistic argument suggests that the sequence is infinite. [Michael Kleber, Jun 23 2004]

REFERENCES

M. Gardner, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..4.

M. Gardner, Letter to N. J. A. Sloane, Nov 16 1979.

Ed T. Prothro, How I Found the Next Pi Prime

Eric Weisstein's World of Mathematics, Pi-Prime

Index entries for sequences related to "constant primes"

Index entries for sequences related to the number Pi

FORMULA

a(n)=floor(10^(A060421(n)-1)*A000796), where A000796 is the constant Pi = 3.14159... _- M. F. Hasler, Sep 02 2013

MAPLE

Digits := 130; n0 := evalf(Pi); for i from 1 to 120 do t1 := trunc(10^i*n0); if isprime(t1) then print(t1); fi; od:

MATHEMATICA

a = {}; Do[k = Floor[Pi 10^n]; If[PrimeQ[k], AppendTo[a, k]], {n, 0, 160}]; a - Artur Jasinski, Mar 26 2008

nn=1000; With[{pidigs=RealDigits[Pi, 10, nn][[1]]}, Select[Table[FromDigits[ Take[pidigs, n]], {n, nn}], PrimeQ]] (* Harvey P. Dale, Sep 26 2012 *)

PROG

(PARI) c=Pi; for(k=0, precision(c), isprime(c\.1^k) & print1(c\.1^k, ", ")) \\ - M. F. Hasler, Sep 01 2013

CROSSREFS

See A060421 for further terms.

Cf. A198018, A198019, A195834, A047777, A053013, A064467.

Sequence in context: A118913 A297480 A282973 * A317482 A136582 A173649

Adjacent sequences:  A005039 A005040 A005041 * A005043 A005044 A005045

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 21 21:51 EDT 2018. Contains 315262 sequences. (Running on oeis4.)