A046284 Primes p such that concatenation of primes from 2 through p is a prime.

2, 3, 7, 719, 1033, 2297, 3037, 11927

Offset

1,1

Comments

"w_n = (P_1)(P_2) ... (P_n) [A019518], by which notation we mean that w_n is constructed in decimal by simple concatenation of digits [much like the Almost Natural numbers (A007376)]. For example, the first few w_n are 2, 23, 235, 2357, 235711, ... ." - Crandall and Pomerance

References

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 72. [The 2002 printing states incorrectly that 5441 is a term.]

Links

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

Eric Weisstein's World of Mathematics, Consecutive Number Sequences.

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Eric Weisstein's World of Mathematics, Smarandache-Wellin Number

Formula

a(n) = prime(A046035(n)) = A000040(A046035(n)).

Example

7 is a term since 2357 is a prime.

Mathematica

a = ""; Do[a = StringJoin[a, ToString[ Prime[n]]]; If[ PrimeQ[ ToExpression[a]], Print[Prime[n]]], {n, 1, 1429}]

Crossrefs

Cf. A000040, A019518, A033308, A069151, A046035.

Sequence in context: A062615 A180162 A129907 * A077524 A069503 A238400

Adjacent sequences: A046281 A046282 A046283 * A046285 A046286 A046287

Keyword

nonn,base,hard,more,changed

Author

Patrick De Geest, Jun 15 1998

Extensions

Additional comments from Robert G. Wilson v, Sep 10 2001

Status

approved