27719 is a member of OEIS A343048: a(n) is the least number whose sum of digits in primorial base equals n, here primorial base is 11 : 10 : 6 : 4 : 2 : 1 and n=34. See blog post Primorial Number Base Revisited.
The sequence can be generated as follows:
INPUT
T=[("number","primorial rep","digit sum")]
T.append(("","",""))
P=[30030,2310,210,30,6,2]
L=[]
n=0
for number in [0..40000]:
original=number
N=[]
for p in P:
N.append(number//p)
number=number%p
if is_odd(original):
N.append(1)
else:
N.append(0)
total=sum(N)
primorial=""
for x in N:
primorial+=str(x)+" "
if total == n:
L.append(original)
n+=1
T.append((original,primorial,sum(N)))
print(L)
print()
print(table(T))
OUTPUT
[0, 1, 3, 5, 11, 17, 23, 29, 59, 89, 119, 149, 179, 209, 419, 629, 839, 1049, 1259, 1469, 1679, 1889, 2099, 2309, 4619, 6929, 9239, 11549, 13859, 16169, 18479, 20789, 23099, 25409, 27719, 30029]
number primorial rep digit sum
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 1 1
3 0 0 0 0 0 1 1 2
5 0 0 0 0 0 2 1 3
11 0 0 0 0 1 2 1 4
17 0 0 0 0 2 2 1 5
23 0 0 0 0 3 2 1 6
29 0 0 0 0 4 2 1 7
59 0 0 0 1 4 2 1 8
89 0 0 0 2 4 2 1 9
119 0 0 0 3 4 2 1 10
149 0 0 0 4 4 2 1 11
179 0 0 0 5 4 2 1 12
209 0 0 0 6 4 2 1 13
419 0 0 1 6 4 2 1 14
629 0 0 2 6 4 2 1 15
839 0 0 3 6 4 2 1 16
1049 0 0 4 6 4 2 1 17
1259 0 0 5 6 4 2 1 18
1469 0 0 6 6 4 2 1 19
1679 0 0 7 6 4 2 1 20
1889 0 0 8 6 4 2 1 21
2099 0 0 9 6 4 2 1 22
2309 0 0 10 6 4 2 1 23
4619 0 1 10 6 4 2 1 24
6929 0 2 10 6 4 2 1 25
9239 0 3 10 6 4 2 1 26
11549 0 4 10 6 4 2 1 27
13859 0 5 10 6 4 2 1 28
16169 0 6 10 6 4 2 1 29
18479 0 7 10 6 4 2 1 30
20789 0 8 10 6 4 2 1 31
23099 0 9 10 6 4 2 1 32
25409 0 10 10 6 4 2 1 33
27719 0 11 10 6 4 2 1 34
30029 0 12 10 6 4 2 1 35
27719 is a Duffinian and cyclic number.
27719 is a xenodrome in base 9 : 42018
27719 can be rendered as a digit equation as follows:
2 - 7 / 7 = 1 ^ 9
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