A019518 Smarandache-Wellin numbers: a(n) is the concatenation of first n primes (written in base 10).

2, 23, 235, 2357, 235711, 23571113, 2357111317, 235711131719, 23571113171923, 2357111317192329, 235711131719232931, 23571113171923293137, 2357111317192329313741, 235711131719232931374143, 23571113171923293137414347

Offset: 1

Author

R. Muller

Keywords

• nonn
• base

Examples

			E.g. a(6) = 2_3_5_7_11_13 = 23571113.
		

References

• 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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..300
• M. Fleuren, Factoring of the Smarandache Concatenated Prime Sequence.
• F. Smarandache, Collected Papers, Vol. II, Tempus Publ. Hse., Bucharest, Romania, 1996.
• Eric Weisstein's World of Mathematics, Consecutive Number Sequences
• Eric Weisstein's World of Mathematics, Copeland-Erdős Constant
• Index entries for sequences related to Most Wanted Primes video

Crossrefs

For the primes in this sequence see A069151. For where the primes occur see A046035.

Cf. A000040, A038394, A046284, A068670 (number of digits).

Programs

Haskell

a019518 n = a019518_list !! (n-1)
a019518_list = map read $ scanl1 (++) $ map show a000040_list :: [Integer]
-- Reinhard Zumkeller, Mar 03 2014

Magma

[Seqint(Reverse(&cat[Reverse(Intseq(NthPrime(k))): k in [1..n]])): n in [1..20]]; // Vincenzo Librandi, Aug 23 2015

Mathematica

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 *)

PARI

s="";for(n=1,30,print1(s=Str(s,prime(n))",")) \\ Cino Hilliard; simplified by M. F. Hasler, Oct 06 2013

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

Extensions

Definition edited by N. J. A. Sloane, Jul 02 2017