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A123568 Prime numbers of the form (10^n - 7)/3. 2
31, 331, 3331, 33331, 333331, 3333331, 33333331, 333333333333333331, 3333333333333333333333333333333333333331, 33333333333333333333333333333333333333333333333331 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The number of initial 3s is n - 1.

Note that each n from 2 to 8 gives primes, but after that the n that correspond to primes are progressively further apart. Singh (1997) gives this as an example of why mathematicians don't trust a preponderance of evidence as proof: in the 17th century, when factoring numbers with as few as eight digits wasn't as easy as it is today, the pattern suggested that all numbers of this form are prime. - Alonso del Arte, Nov 11 2012

REFERENCES

Simon Singh, Fermat's Enigma. New York: Walker & Company (1997) p. 159.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..17

EXAMPLE

a(7) = 33333331 because that is the seventh number of the specified form to be prime.

333333331 is not in the sequence because it is composite, being the product of 17 and 19607843.

MATHEMATICA

Do[If[PrimeQ[(10^n - 7)/3], Print[(10^n - 7)/3]], {n, 1, 100}] (* Jasinski *)

Select[(10^Range[50] - 7)/3, PrimeQ[#] &] (* Alonso del Arte, Nov 11 2012 *)

Select[Table[FromDigits[PadLeft[{1}, n, 3]], {n, 50}], PrimeQ] (* Harvey P. Dale, Dec 05 2018 *)

PROG

(PARI) select(ispseudoprime, vector(20, n, (10^n-7)/3)) \\ Charles R Greathouse IV, Nov 12 2012

CROSSREFS

Cf. A055557, A051200, A033175, A065586, A068104.

Sequence in context: A138697 A186071 A033175 * A111675 A142495 A100728

Adjacent sequences:  A123565 A123566 A123567 * A123569 A123570 A123571

KEYWORD

nonn

AUTHOR

Artur Jasinski, Nov 12 2006

STATUS

approved

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Last modified October 19 22:55 EDT 2019. Contains 328244 sequences. (Running on oeis4.)