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A003618 Largest n-digit prime.
(Formerly M4452)
34
7, 97, 997, 9973, 99991, 999983, 9999991, 99999989, 999999937, 9999999967, 99999999977, 999999999989, 9999999999971, 99999999999973, 999999999999989, 9999999999999937, 99999999999999997, 999999999999999989, 9999999999999999961 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Alonso del Arte, Dec 03 2017: (Start)

Since 10^n - 1 is always a multiple of 9, one could be tempted to think that 9 is the least frequently occurring least significant digit in terms of this sequence.

The terms shown above suggest the hypothesis is false. Eight have 7 for a least significant digit, four have 1, another four have 9, and 3 is the least frequently occurring least significant digit, with only three instances. (End)

REFERENCES

O'Hara, J. Rec. Math., 22 (1990), Table on page 278.

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..200 [Jon E. Schoenfield verified that these numbers are indeed all primes, Feb 02 2009]

Eric Weisstein's World of Mathematics, Previous Prime

R. G. Wilson, v., Extract from letter to N. J. A. Sloane, May 20 1994, with annotated scanned copy of page 278 of O'Hara article.

EXAMPLE

No power of 10 is prime.

9 = 3^2, 8 = 2^3 but 7 is prime, so a(1) = 7.

99 = 3^2 * 11 but 97 is prime, so a(2) = 97.

999 = 3^3 * 37 but 997 is prime, so a(3) = 997.

9999 = 3^2 * 11 * 101, 9997 = 13 * 769, 9995 = 5 * 1999, 9993 = 3 * 3331, 9991 = 97 * 103, ..., 9975 = 5^2 * 399, but 9973 is prime, so a(4) = 9973.

MATHEMATICA

NextPrime[10^Range[20], -1] (* Harvey P. Dale, Feb 03 2011 *)

PROG

(PARI) a(n)=precprime(10^n) \\ Charles R Greathouse IV, Jul 19 2011

(MAGMA) [PreviousPrime(10^n): n in [1..20]]; // Vincenzo Librandi, Sep 13 2016

CROSSREFS

Cf. A003617, A033874.

Sequence in context: A125590 A068694 A158579 * A173833 A093172 A074110

Adjacent sequences:  A003615 A003616 A003617 * A003619 A003620 A003621

KEYWORD

nonn,nice,base

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

More terms from Stefan Steinerberger, Apr 08 2006

STATUS

approved

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Last modified December 18 14:30 EST 2018. Contains 318229 sequences. (Running on oeis4.)