A072125 -id:A072125 - cp's OEIS frontend

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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

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