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 A371565 Integers k such that removing the even digits from k! yields a prime number. 0
 6, 7, 8, 9, 10, 13, 18, 20, 21, 23, 25, 82, 119, 137, 2389, 4108, 5875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For k > 4, the number k! is divisible by 10. In fact, for k > 1, the final nonzero digit of k! is even (see A008904). Then, if the even digits of k! are removed, the result is either 0 or an odd number, where the latter are candidates for prime numbers. Thus, with this procedure, it is possible to obtain the following prime numbers, although not in this order of occurrence: 3, 5, 7, 3917, 373757, 5517397, 519917179, 155111333959. LINKS Table of n, a(n) for n=1..17. EXAMPLE 13 is a term since 13! = 6227020800 and eliminating the even digits yields the number 7, which is prime. 18 is a term since 18! = 6402373705728000 and eliminating the even digits yields 373757, which is prime. MATHEMATICA q[n_] := PrimeQ[FromDigits[Select[IntegerDigits[n!], OddQ]]]; Select[Range[200], q] (* Amiram Eldar, Mar 30 2024 *) PROG (Python) from sympy import isprime from math import factorial def ok(n): r = "".join(d for d in str(factorial(n)) if d in "13579") return len(r) and isprime(int(r)) print([k for k in range(1000) if ok(k)]) # Michael S. Branicky, Mar 27 2024 (Python) # generator of terms, removing trailing 0's from n! from sympy import isprime from itertools import count, islice def agen(): f = 1 for n in count(1): f *= n q, t = divmod(f, 10) while t == 0: f = q q, t = divmod(f, 10) r = "".join(d for d in str(f) if d in "13579") if len(r) and isprime(int(r)): yield n print(list(islice(agen(), 14))) # Michael S. Branicky, Apr 10 2024 (PARI) isok(k) = my(d=digits(k!)); ispseudoprime(fromdigits(select(x->(x%2), d))); \\ Michel Marcus, Mar 30 2024 CROSSREFS Cf. A000040, A000142. Sequence in context: A069838 A067901 A115840 * A353437 A352155 A058368 Adjacent sequences: A371562 A371563 A371564 * A371566 A371567 A371568 KEYWORD nonn,base,more AUTHOR Gonzalo Martínez, Mar 27 2024 EXTENSIONS a(12)-a(17) from Michael S. Branicky, Mar 27 2024 STATUS approved

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Last modified August 9 14:37 EDT 2024. Contains 375042 sequences. (Running on oeis4.)