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

1,1

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

Table of n, a(n) for n=1..7.

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

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 *)

Prog

(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

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.

Sequence in context: A069207 A168671 A136197 * A175664 A053690 A177948

Adjacent sequences: A071617 A071618 A071619 * A071621 A071622 A071623

Keyword

nonn,base,hard,more

Author

Robert G. Wilson v, Jun 21 2002

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

Status

approved