OFFSET
1,1
COMMENTS
Bugeaud proves that the largest prime factor in a(n) increases without bound; in particular, for any e > 0 and all large n, the largest prime factor in a(n) is (1-e) * log log a(n) * log log log a(n) / log log log log a(n). So the largest prime factor in a(n) is more than k log n log log n/log log log n for any k < 1/3 and large enough n.
It appears that a(49) = 64 is the largest power of 2 in the sequence, a(78) = 96 is the largest 3-smooth number in this sequence, a(113) = 405 is the largest 5-smooth number in this sequence, a(170) = 1008 is the largest 7- and 11-smooth number in this sequence, a(243) = 9009 is the largest 13-smooth number in this sequence, a(259) = 20007 is the largest 19-smooth number in this sequence, etc.
LINKS
Yann Bugeaud, On the digital representation of integers with bounded prime factors, Osaka J. Math. 55 (2018), 315-324; arXiv:1609.07926 [math.NT], 2016.
FORMULA
Numbers of the form a*10^b + c where 0 < a,c < 10 and b > 0.
PROG
(PARI) a(n)=my(t=divrem(n-1, 81)); 10*(t[2]\9+1)*10^t[1]+t[2]%9+1
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Charles R Greathouse IV, Jan 20 2023
STATUS
approved