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