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A071620 Integer lengths of the Champernowne primes (concatenation of first a(n) entries (digits) of A033307 is prime). 5
10, 14, 24, 235, 2804, 4347, 37735 (list; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified May 18 02:52 EDT 2024. Contains 372617 sequences. (Running on oeis4.)