A082549 Numbers k such that concatenation of first k primes, separated by zeros, is prime.

1, 9, 15, 25, 59, 444

Offset

1,2

Comments

Let w_k = (p_1)0(p_2)0(p_3)...0(p_k), where p_i is the i-th prime. k is a term if w_k is prime.

a(7) > 2615. - Derek Orr, Aug 12 2014

a(7) > 15000. - Michael S. Branicky, May 07 2025

Links

Table of n, a(n) for n=1..6.

Example

a(1) = 2 is a term because the first prime by itself, p_1 = 2, is prime.
a(2) = 9 because the concatenation of the first 9 primes separated by zeros is (p_1)0(p_2)0..0(p_9) = 2030507011013017019023, which is prime.

Mathematica

Select[Range[450], PrimeQ[FromDigits[Flatten[IntegerDigits/@Riffle[ Prime[ Range[ #]], 0]]]]&] (* Harvey P. Dale, Feb 28 2020 *)

Prog

(PARI)
p=""; for(n=1, 5000, p=concat(p, "0"); p=concat(p, Str(prime(n))); if(ispseudoprime(eval(p)), print1(n, ", "))) \\ Derek Orr, Aug 12 2014

Crossrefs

Sequence in context: A193227 A014003 A333788 * A013569 A129401 A164385

Adjacent sequences: A082546 A082547 A082548 * A082550 A082551 A082552

Keyword

nonn,base,hard,more

Author

Farideh Firoozbakht, May 03 2003

Status

approved