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A344888
a(n) is the least base k >= 2 where n is an undulating number (i.e., with digits of the form abababab...).
1
2, 2, 2, 2, 3, 2, 3, 2, 3, 4, 2, 4, 4, 3, 4, 2, 3, 4, 5, 5, 3, 2, 5, 3, 5, 4, 3, 6, 6, 4, 3, 2, 6, 6, 4, 6, 5, 6, 4, 7, 3, 5, 2, 6, 7, 7, 4, 7, 7, 6, 3, 4, 5, 8, 8, 4, 8, 5, 8, 4, 3, 6, 5, 2, 7, 8, 9, 5, 4, 9, 3, 7, 5, 8, 6, 9, 9, 9, 5, 9, 3, 8, 9, 5, 10, 2, 6
OFFSET
0,1
LINKS
FORMULA
a(n) <= A000196(n) + 1 for any n > 0.
a(n) <= 10 for any n in A033619.
a(n) = 2 iff n belongs to A000225 or to A000975.
EXAMPLE
For n = 49:
- we have:
b 49 in base b Undulating?
- ------------ -----------
2 110001 No
3 1211 No
4 301 No
5 144 No
6 121 Yes
- so a(49) = 6.
PROG
(PARI) is(n, base=10) = my (d=digits(n, base)); #d<=2 || d[1..#d-2]==d[3..#d]
a(n) = for (b=2, oo, if (is(n, b), return (b)))
(Python)
def A344888(n):
b, m = 2, n
while True:
m, x = divmod(m, b)
m, y = divmod(m, b)
while m > 0:
m, z = divmod(m, b)
if z != x:
break
if m > 0:
m, z = divmod(m, b)
if z != y:
break
else:
return b
else:
return b
b += 1
m = n # Chai Wah Wu, Jun 02 2021
CROSSREFS
KEYWORD
nonn,look,base
AUTHOR
Rémy Sigrist, Jun 01 2021
STATUS
approved