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A152242
Integers formed by concatenating primes.
13
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
1,1
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
LINKS
EXAMPLE
101 is a member since it is prime; 303 is not since it is composite and 30 is also not a prime.
PROG
(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)
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
KEYWORD
nonn,base
AUTHOR
Eric Angelini, Oct 15 2009
EXTENSIONS
More terms from M. F. Hasler and Zak Seidov, Oct 15 2009
STATUS
approved