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%I #56 May 13 2023 19:59:59
%S 1,2,4,128,174,342,435,1429
%N Numbers k such that the concatenation of the first k primes (A019518) is a prime.
%C No other terms with k <= 34736. - _Eric W. Weisstein_, Oct 30 2015
%D R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 72. [The 2002 printing states incorrectly that 719 is a term.]
%H M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/SmConPri.txt">Smarandache Concatenated Primes</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConsecutiveNumberSequences.html">Consecutive Number Sequences</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Smaradache-WellinPrime.html">Smaradache-Wellin Prime</a>
%H <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>
%F a(n) = A000720(A046284(n)), or A046284(n) = prime(a(n)).
%e 4 is a term since 2357 is a prime. [Corrected by Ed Murphy (emurphy42(AT)socal.rr.com), May 15 2007]
%t max = 1500; With[{primes = Prime[Range[max]]}, Flatten[Position[ Table[ FromDigits[Flatten[IntegerDigits/@Take[primes, n]]], {n, max}], _?PrimeQ]]] (* _Harvey P. Dale_, Dec 17 2013 *)
%t Position[FromDigits /@ Rest[FoldList[Join, {}, IntegerDigits[Prime[Range[ 10^3]]]]], _?PrimeQ] // Flatten (* _Eric W. Weisstein_, Oct 30 2015 *)
%o (PARI) p=""; for(n=1, 2000, p=concat(p, prime(n)); if(ispseudoprime(eval(p)), print1(n", "))) \\ _Altug Alkan_, Oct 30 2015
%Y Cf. A019518, A069151, A046284.
%Y Cf. A033308 (Decimal expansion of Copeland-Erdős constant: concatenate primes).
%K nonn,base,nice
%O 1,2
%A _Eric W. Weisstein_
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