A052056 Numbers k such that k! starts with its largest prime substring.

2, 4, 6, 7, 9, 10, 15, 16, 20, 21, 23, 25, 30, 35, 43, 78, 102, 105, 132, 138, 151, 189, 202, 215, 219, 233, 241, 264, 320, 334, 349, 352, 367, 386, 433, 458, 520, 583, 779, 885, 905, 1068, 1078, 1131, 1149, 1198, 1271, 1276, 1314, 1503, 1623, 1646, 1903, 1962, 2053

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base

Examples

			16 is a term because 16! = {209227}89888000 and its largest prime substring 209227 starts from the left.
		

Links

• Michael S. Branicky, Python program

Crossrefs

Cf. A000142, A046277.

Programs

Python

from sympy import isprime
def starts_with_lps(n): # see link for faster version
    s = str(n)
    ss = (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1))
    lps = max((u for u in (int(t) for t in ss) if isprime(u)), default=0)
    return lps > 0 and s.startswith(str(lps))
def afind():
    k, fk = 1, 1
    while True:
        if starts_with_lps(fk):
            print(k, end=", ")
        k += 1
        fk *= k
afind() # Michael S. Branicky, Dec 31 2021

Extensions

More terms from Sean A. Irvine, Feb 16 2011

Offset changed to 1 by Jon E. Schoenfield, Oct 17 2019

a(38)-a(49) from Michael S. Branicky, Dec 31 2021

a(50)-a(55) from Michael S. Branicky, May 31 2023