A019549 Primes formed by concatenating other primes.

23, 37, 53, 73, 113, 137, 173, 193, 197, 211, 223, 227, 229, 233, 241, 257, 271, 277, 283, 293, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 433, 523, 541, 547, 557, 571, 577, 593, 613, 617, 673, 677, 719, 727, 733, 743, 757, 761, 773, 797, 977

Offset

1,1

Links

M. F. Hasler, Table of n, a(n) for n = 1..17495

Sylvester Smith, A Set of Conjectures on Smarandache Sequences, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.

Example

113 is member as 11 and 3 are primes.
a(12)=227 = "2"+"2"+"7" is the first term not in A105184 (restricted to concatenation of two primes). [M. F. Hasler, Oct 15 2009]

Prog

(PARI) is_A019549(n, recurse=0)={ isprime(n) == recurse & return(recurse); for(i=1, #Str(n)-1, isprime( n%10^i ) & is_A019549( n\10^i, 1) & n\10^(i-1)%10 & return(1)) } \\ M. F. Hasler, Oct 15 2009
(Python)
def c(n, m):
    if m > 0 and isprime(n): return True
    s = str(n)
    return any(s[i]!="0" and isprime(int(s[:i])) and c(int(s[i:]), m+1) for i in range(1, len(s)))
def ok(n): return isprime(n) and c(n, 0)
print([k for k in range(978) if ok(k)]) # Michael S. Branicky, Sep 01 2024

Crossrefs

Cf. A105184, A152242.

Sequence in context: A051362 A034302 A057878 * A272157 A129800 A105184

Adjacent sequences: A019546 A019547 A019548 * A019550 A019551 A019552

Keyword

nonn,base

Author

R. Muller

Status

approved