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A046035 Numbers n such that the concatenation of the first n primes (A019518) is a prime. 11
1, 2, 4, 128, 174, 342, 435, 1429 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The primes themselves (A069151) are sometimes called Smarandache-Wellin primes.

No others with n <= 34736. - Eric W. Weisstein, Oct 30 2015

REFERENCES

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.]

LINKS

Table of n, a(n) for n=1..8.

M. Fleuren, Smarandache Concatenated Primes.

Eric Weisstein's World of Mathematics, Consecutive Number Sequences

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Eric Weisstein's World of Mathematics, Smaradache-Wellin Prime

FORMULA

A046284(n) = prime(a(n)).

EXAMPLE

4 is a term since 2357 is a prime. [Corrected by Ed Murphy (emurphy42(AT)socal.rr.com), May 15 2007]

MATHEMATICA

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 *)

Position[FromDigits /@ Rest[FoldList[Join, {}, IntegerDigits[Prime[Range[ 10^3]]]]], _?PrimeQ] // Flatten (* Eric W. Weisstein, Oct 30 2015 *)

PROG

(PARI) p=""; for(n=1, 2000, p=concat(p, prime(n)); if(ispseudoprime(eval(p)), print1(n", "))) \\ Altug Alkan, Oct 30 2015

CROSSREFS

Cf. A019518 (Smarandache-Wellin numbers).

Cf. A033308 (Decimal expansion of Copeland-Erdős constant: concatenate primes).

Cf. A069151 (Smarandache-Wellin primes; Concatenations of consecutive primes, starting with 2, that are also prime).

Sequence in context: A259381 A009595 A018493 * A134710 A009073 A012561

Adjacent sequences:  A046032 A046033 A046034 * A046036 A046037 A046038

KEYWORD

nonn,base,nice

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified May 3 14:25 EDT 2016. Contains 272361 sequences.