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%I #10 Feb 25 2024 11:01:14
%S 1,13,15,30,31,91,101,110,128,133,136,138,144,152,156,166,175,193,199,
%T 203,215,230,250,260,280,281,303,304,306,307,309,315,320,330,331,340,
%U 361,391,412,508,520,550,606,651,661,681,708,712,717,730,750,751,780
%N Numbers k such that concatenating k and the sum of factorials of the digits of k produces a prime.
%C The largest prime I have found pertaining to this sequence is A109016(Fibonacci(9837)) with 2064 digits (not proved prime, only Fermat and Lucas PRP).
%H Michael S. Branicky, <a href="/A108257/b108257.txt">Table of n, a(n) for n = 1..10000</a>
%e 193 is in the sequence because 1!+9!+3! = 362887 and 193362887 is prime.
%t Select[Range[780],PrimeQ[FromDigits[Join[IntegerDigits[#],IntegerDigits[Total[IntegerDigits[#]!]]]]]&] (* _James C. McMahon_, Feb 22 2024 *)
%o (Python)
%o from math import factorial
%o from sympy import isprime
%o def ok(n):
%o return isprime(int((s:=str(n))+str(sum(factorial(int(d)) for d in s))))
%o print([k for k in range(999) if ok(k)]) # _Michael S. Branicky_, Feb 22 2024
%Y Cf. A061602, A109016.
%K base,nonn
%O 1,2
%A _Jason Earls_, Jun 18 2005
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