A038687 -id:A038687 - cp's OEIS frontend

A236403 Numbers not in A236402.

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, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset: 1

Eric Angelini, Jan 30 2014

This sequence has density 0, since all numbers except a thin fraction have digits 0 through 18 in base 100. In particular, there are at most x^0.99782 members up to x for large enough x. (This can be improved.) - Charles R Greathouse IV, Jan 30 2014
Where does this first differ from A038687? - R. J. Mathar, Feb 03 2014
Is this a shifted version of A031954? - R. J. Mathar, Feb 03 2014

Subsequence of A052382.

Cf. A236402.

is(n)=my(d=digits(n), S=Set(d), v=List()); for(i=2, #d, listput(v, 10*d[i-1]+d[i])); S=setunion(S,Set(v)); for(i=2, #d, if(!setsearch(S, d[i-1]+d[i]), return(1))); 0 \\ Charles R Greathouse IV, Mar 10 2021

def ok(n):
  s = str(n)
  return not all(str(sum(map(int, s[i:i+2]))) in s for i in range(len(s)-1))
print(list(filter(ok, range(120)))) # Michael S. Branicky, Jun 11 2021

Missing a(82) added by Charles R Greathouse IV, Mar 10 2021

A359983 Numbers with exactly two nonzero decimal digits and not ending with 0.

Original entry on oeis.org

Offset: 1

Charles R Greathouse IV, Jan 20 2023

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.

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.

Cf. A359651, A359098. Subsequence of A038687.

a(n)=my(t=divrem(n-1,81)); 10*(t[2]\9+1)*10^t[1]+t[2]%9+1

Numbers of the form a*10^b + c where 0 < a,c < 10 and b > 0.

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A236403 Numbers not in A236402.

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