A265043 -id:A265043 - cp's OEIS frontend

A176942 Champernowne primes.

1234567891, 12345678910111, 123456789101112131415161

Offset: 1

Marco Ripà, Jan 27 2011

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

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

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

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.

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 *)

A071620 Integer lengths of the Champernowne primes (concatenation of first a(n) entries (digits) of A033307 is prime).

Original entry on oeis.org

10, 14, 24, 235, 2804, 4347, 37735

Offset: 1

Robert G. Wilson v, Jun 21 2002

Next term has n > 113821. - Eric W. Weisstein, Nov 04 2015

Also: concatenation of A007376(1 .. a(n)) is prime. - M. F. Hasler, Oct 23 2019

Eric Weisstein's World of Mathematics, Champernowne Constant Digits
Eric Weisstein's World of Mathematics, Consecutive Number Sequences
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

Cf. A007376 (infinite Barbier word = almost-natural numbers: write n in base 10 and juxtapose digits).
Cf. A033307 (decimal expansion of Champernowne constant), A176942 (the corresponding primes of length a(n)), A265043.
Cf. A072125.

f[0] = 0; f[n_Integer] := 10^(Floor[Log[10, n]] + 1)*f[n - 1] + n; Do[If[PrimeQ[FromDigits[Take[IntegerDigits[f[n]], n]]], Print[n]], {n, 1, 3000}]
Cases[FromDigits /@ Rest[FoldList[Append, {}, RealDigits[N[ChampernowneNumber[], 1000]][[1]]]],  p_?PrimeQ :> IntegerLength[p]] (* Eric W. Weisstein, Nov 04 2015 *)

from itertools import count, islice
from sympy import isprime
def A071620_gen(): # generator of terms
    c, l = 0, 0
    for n in count(1):
        for d in str(n):
            c = 10*c+int(d)
            l += 1
            if isprime(c):
                yield l
A071620_list = list(islice(A071620_gen(),5)) # Chai Wah Wu, Feb 27 2023

Edited by Charles R Greathouse IV, Apr 28 2010
a(6) = 4347 from Eric W. Weisstein, Jul 14 2013
a(7) = 37735 from Eric W. Weisstein, Jul 15 2013

cp's OEIS Frontend

A176942 Champernowne primes.

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