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A019518
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Smarandache-Wellin numbers: a(n) is the concatenation of first n primes (written in base 10).
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84
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2, 23, 235, 2357, 235711, 23571113, 2357111317, 235711131719, 23571113171923, 2357111317192329, 235711131719232931, 23571113171923293137, 2357111317192329313741, 235711131719232931374143, 23571113171923293137414347
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OFFSET
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1,1
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REFERENCES
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R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 72. [The 2002 printing states incorrectly that a(719) is prime. Cf. A046035.] This book uses the name "Smarandache-Wellin numbers", referring to a 1998 private communication from P. Wellin.
H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.
M. Le, On Smarandache Concatenated Sequences I: Prime Power Sequences, Smarandache Notions Journal, Vol. 9, No. 1-2, 1998, 129-130.
S. Smarandoiu, Convergence of Smarandache continued fractions, Abstract 96T-11-195, Abstracts Amer. Math. Soc., 17 (No. 4, 1996), 680.
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LINKS
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EXAMPLE
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E.g. a(6) = 2_3_5_7_11_13 = 23571113.
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MATHEMATICA
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ConsecutivePrimes[n_] := FromDigits[Flatten[IntegerDigits /@ Prime[Range[n]]]] (* Eric W. Weisstein *)
Table[FromDigits[Flatten[IntegerDigits[Prime[Range[i]]]]], {i, 15}] (* Jayanta Basu, May 30 2013 *)
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PROG
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(PARI) A019518(n)=eval(concat(concat([""], primes(n)))) \\ Faster than concat(apply(s->Str(s), primes(n))) or forprime(...s=Str(s, p)). - M. F. Hasler, Oct 06 2013
(Haskell)
a019518 n = a019518_list !! (n-1)
a019518_list = map read $ scanl1 (++) $ map show a000040_list :: [Integer]
(Magma) [Seqint(Reverse(&cat[Reverse(Intseq(NthPrime(k))): k in [1..n]])): n in [1..20]]; // Vincenzo Librandi, Aug 23 2015
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CROSSREFS
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For the primes in this sequence see A069151. For where the primes occur see A046035.
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KEYWORD
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nonn,base
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AUTHOR
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R. Muller
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EXTENSIONS
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STATUS
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approved
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