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A173688
Numbers m such that the sum of square of factorial of decimal digits is prime.
2
10, 11, 12, 13, 14, 15, 19, 20, 21, 30, 31, 40, 41, 50, 51, 90, 91, 100, 101, 110, 111, 123, 132, 133, 134, 135, 138, 143, 144, 147, 153, 156, 158, 165, 168, 169, 174, 177, 183, 185, 186, 196, 203, 213, 230, 231, 302, 303, 304, 305, 308, 312, 313, 314, 315, 318, 320
OFFSET
1,1
COMMENTS
Let the decimal expansion of m = d(0)d(1)...d(p). Numbers such that Sum_{k=0..p} (d(k)!)^2 is prime.
LINKS
EXAMPLE
a(5) = 14 is in the sequence because (1!)^2 + (4!)^2 = 1 + 24^2 = 577 and 577 is prime.
MAPLE
with(numtheory):for n from 1 to 500 do:l:=length(n):n0:=n:s:=0:for m from 1
to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+(u!)^2:od: if type(s, prime)=true
then printf(`%d, `, n):else fi:od:
MATHEMATICA
Select[Range[400], PrimeQ[Total[(IntegerDigits[#]!)^2]]&] (* Harvey P. Dale, Mar 23 2011 *)
PROG
(Python)
from itertools import count, islice, combinations_with_replacement
from math import factorial
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def A173688_gen(): # generator of terms
for l in count(0):
for i in range(1, 10):
fi = factorial(i)**2
yield from sorted(int(str(i)+''.join(map(str, k))) for j in combinations_with_replacement(range(10), l) for k in multiset_permutations(j) if isprime(fi+sum(map(lambda n:factorial(n)**2, j))))
A173688_list = list(islice(A173688_gen(), 50)) # Chai Wah Wu, Feb 23 2023
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Nov 25 2010
STATUS
approved