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

%I A071620 #55 Feb 16 2025 08:32:46
%S A071620 10,14,24,235,2804,4347,37735
%N A071620 Integer lengths of the Champernowne primes (concatenation of first a(n) entries (digits) of A033307 is prime).
%C A071620 Next term has n > 113821. - _Eric W. Weisstein_, Nov 04 2015
%C A071620 Also: concatenation of A007376(1 .. a(n)) is prime. - _M. F. Hasler_, Oct 23 2019
%H A071620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChampernowneConstantDigits.html">Champernowne Constant Digits</a>
%H A071620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConsecutiveNumberSequences.html">Consecutive Number Sequences</a>
%H A071620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConstantPrimes.html">Constant Primes</a>
%H A071620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H A071620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandachePrime.html">Smarandache Prime</a>
%t A071620 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}]
%t A071620 Cases[FromDigits /@ Rest[FoldList[Append, {}, RealDigits[N[ChampernowneNumber[], 1000]][[1]]]],  p_?PrimeQ :> IntegerLength[p]] (* _Eric W. Weisstein_, Nov 04 2015 *)
%o A071620 (Python)
%o A071620 from itertools import count, islice
%o A071620 from sympy import isprime
%o A071620 def A071620_gen(): # generator of terms
%o A071620     c, l = 0, 0
%o A071620     for n in count(1):
%o A071620         for d in str(n):
%o A071620             c = 10*c+int(d)
%o A071620             l += 1
%o A071620             if isprime(c):
%o A071620                 yield l
%o A071620 A071620_list = list(islice(A071620_gen(),5)) # _Chai Wah Wu_, Feb 27 2023
%Y A071620 Cf. A007376 (infinite Barbier word = almost-natural numbers: write n in base 10 and juxtapose digits).
%Y A071620 Cf. A033307 (decimal expansion of Champernowne constant), A176942 (the corresponding primes of length a(n)), A265043.
%Y A071620 Cf. A072125.
%K A071620 nonn,base,hard,more
%O A071620 1,1
%A A071620 _Robert G. Wilson v_, Jun 21 2002
%E A071620 Edited by _Charles R Greathouse IV_, Apr 28 2010
%E A071620 a(6) = 4347 from _Eric W. Weisstein_, Jul 14 2013
%E A071620 a(7) = 37735 from _Eric W. Weisstein_, Jul 15 2013