cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A082549 #15 May 07 2025 08:29:24
%S A082549 1,9,15,25,59,444
%N A082549 Numbers k such that concatenation of first k primes, separated by zeros, is prime.
%C A082549 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.
%C A082549 a(7) > 2615. - _Derek Orr_, Aug 12 2014
%C A082549 a(7) > 15000. - _Michael S. Branicky_, May 07 2025
%e A082549 a(1) = 2 is a term because the first prime by itself, p_1 = 2, is prime.
%e A082549 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.
%t A082549 Select[Range[450],PrimeQ[FromDigits[Flatten[IntegerDigits/@Riffle[ Prime[ Range[ #]],0]]]]&] (* _Harvey P. Dale_, Feb 28 2020 *)
%o A082549 (PARI)
%o A082549 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
%K A082549 nonn,base,hard,more
%O A082549 1,2
%A A082549 _Farideh Firoozbakht_, May 03 2003