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

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

Offset: 1

Author

Robert G. Wilson v, Jun 21 2002

Keywords

• nonn
• base
• hard
• more

Comments

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

Links

• 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

Crossrefs

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.

Programs

Mathematica

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 *)

Python

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

Extensions

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