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

1,1

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

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

Sequence in context: A309706 A240959 A054261 * A048677 A132933 A220373

Adjacent sequences: A019515 A019516 A019517 * A019519 A019520 A019521

Keyword

nonn,base

Author

R. Muller

Extensions

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

Status

approved