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

%I A052056 #18 May 31 2023 21:31:20
%S A052056 2,4,6,7,9,10,15,16,20,21,23,25,30,35,43,78,102,105,132,138,151,189,
%T A052056 202,215,219,233,241,264,320,334,349,352,367,386,433,458,520,583,779,
%U A052056 885,905,1068,1078,1131,1149,1198,1271,1276,1314,1503,1623,1646,1903,1962,2053
%N A052056 Numbers k such that k! starts with its largest prime substring.
%H A052056 Michael S. Branicky, <a href="/A052056/a052056.py.txt">Python program</a>
%e A052056 16 is a term because 16! = {209227}89888000 and its largest prime substring 209227 starts from the left.
%o A052056 (Python)
%o A052056 from sympy import isprime
%o A052056 def starts_with_lps(n): # see link for faster version
%o A052056     s = str(n)
%o A052056     ss = (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1))
%o A052056     lps = max((u for u in (int(t) for t in ss) if isprime(u)), default=0)
%o A052056     return lps > 0 and s.startswith(str(lps))
%o A052056 def afind():
%o A052056     k, fk = 1, 1
%o A052056     while True:
%o A052056         if starts_with_lps(fk):
%o A052056             print(k, end=", ")
%o A052056         k += 1
%o A052056         fk *= k
%o A052056 afind() # _Michael S. Branicky_, Dec 31 2021
%Y A052056 Cf. A000142, A046277.
%K A052056 nonn,base
%O A052056 1,1
%A A052056 _Patrick De Geest_, Jan 15 2000
%E A052056 More terms from _Sean A. Irvine_, Feb 16 2011
%E A052056 Offset changed to 1 by _Jon E. Schoenfield_, Oct 17 2019
%E A052056 a(38)-a(49) from _Michael S. Branicky_, Dec 31 2021
%E A052056 a(50)-a(55) from _Michael S. Branicky_, May 31 2023