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A359983
Numbers with exactly two nonzero decimal digits and not ending with 0.
0
11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 201
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
Cf. A359651, A359098. Subsequence of A038687.
Sequence in context: A162903 A216589 A038687 * A236403 A293728 A070255
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved