A152242 Integers formed by concatenating primes.

2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 47, 52, 53, 55, 57, 59, 61, 67, 71, 72, 73, 75, 77, 79, 83, 89, 97, 101, 103, 107, 109, 112, 113, 115, 117, 127, 131, 132, 133, 135, 137, 139, 149, 151, 157, 163, 167, 172, 173, 175, 177, 179

Offset: 1

Author

Eric Angelini, Oct 15 2009

Keywords

• nonn
• base

Comments

Leading zeros are not allowed (cf. A166504).

For any k > 0, there are A246806(k) terms with k digits. - Rémy Sigrist, Jan 08 2023

Examples

			101 is a member since it is prime; 303 is not since it is composite and 30 is also not a prime.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Henri Picciotto, Selected Integer Sequences

Crossrefs

Cf. A019549, A038692, A066737, A105184, A129800, A166504, A246806.

Programs

PARI

is_A152242(n)=/* If n is even, the last digit must be 2 and [n\10] (if nonzero) must be in this sequence. (This check is not necessary but improves speed.) */ bittest(n,0) || return( n%10==2 && (n<10 || is_A152242(n\10))); isprime(n) && return(1); for(i=1,#Str(n)-1, n%10^i>10^(i-1) && isprime( n%10^i ) && is_A152242( n\10^i) && return(1)) \\ M. F. Hasler, Oct 15 2009; edited Oct 16 2009, to disallow leading zeros

Python

from sympy import isprime
def ok(n):
    if isprime(n): return True
    s = str(n)
    return any(s[i]!="0" and isprime(int(s[:i])) and ok(int(s[i:])) for i in range(1, len(s)))
print([k for k in range(180) if ok(k)]) # Michael S. Branicky, Sep 01 2024

Extensions

More terms from M. F. Hasler and Zak Seidov, Oct 15 2009