A176942 Champernowne primes.

1234567891, 12345678910111, 123456789101112131415161

Offset: 1

Author

Marco Ripà, Jan 27 2011

Keywords

• base
• nonn

Comments

Primes formed from an initial portion 1234... of the infinite string 12345678910111213... of the concatenation of all positive integers (decimal digits of the Champernowne constant).

From Eric W. Weisstein, Jul 15 2013: (Start)

The next terms are too big to display:

a(4) = 123456789...1121131141 (235 digits)

a(5) = 123456789...6896997097 (2804 digits)

a(6) = 12345...13611362136313 (4347 digits)

a(7) = 123456789...9709971097 (37735 digits)

a(8) has more than 37800 digits. (End)

a(8) has more than 140000 digits. - Tyler Busby, Feb 12 2023

References

• R. W. Stephan, Factors and primes in two Smarandache sequences.

Links

• Eric W. Weisstein, Table of n, a(n) for n = 1..6
• Eric W. Weisstein, Table of n, a(n) for n = 1..7 (an a-file)
• Eric Weisstein's World of Mathematics, Champernowne Constant
• Eric Weisstein's World of Mathematics, Constant Primes
• Eric Weisstein's World of Mathematics, Integer Sequence Primes
• Eric Weisstein's World of Mathematics, Smarandache Prime

Crossrefs

Cf. A007908, A058183, A073175, A053546.

Cf. A007376 (infinite Barbier word = almost-natural numbers: write n in base 10 and juxtapose digits).

Cf. A033307 (decimal expansion of Champernowne constant).

Cf. A071620 (number of digits in the n-th Champernowne prime).

See A265043 for where to end the string of numbers that are being concatenated in order to get the n-th prime.

Programs

Mathematica

With[{no=500},FromDigits/@Select[Table[Take[Flatten[IntegerDigits/@Range[no]],n],{n,no}],PrimeQ[FromDigits[#]]&]]  (* Harvey P. Dale, Feb 06 2011 *)
Select[Table[Floor[N[ChampernowneNumber[10], n]*10^n], {n, 24}], PrimeQ] (* Arkadiusz Wesolowski, May 10 2012 *)