cp's OEIS Frontend

A359651 Numbers with exactly three nonzero decimal digits and not ending with 0.

%I A359651 #14 Jan 15 2023 02:37:05
%S A359651 111,112,113,114,115,116,117,118,119,121,122,123,124,125,126,127,128,
%T A359651 129,131,132,133,134,135,136,137,138,139,141,142,143,144,145,146,147,
%U A359651 148,149,151,152,153,154,155,156,157,158,159,161,162,163,164,165,166,167,168,169,171,172,173,174,175
%N A359651 Numbers with exactly three nonzero decimal digits and not ending with 0.
%C A359651 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.
%C A359651 It appears that a(1293) = 4096 is the largest power of 2 in the sequence, a(1349) = 4608 is the largest 3-smooth number in this sequence, a(1598) = 6075 is the largest 5-smooth number in this sequence, a(5746) = 500094 is the largest 7- and 11-smooth number in this sequence, a(9158) = 5010005 is the largest 13-smooth member in this sequence, etc.
%H A359651 Yann Bugeaud, <a href="https://arxiv.org/abs/1609.07926">On the digital representation of integers with bounded prime factors</a>, Osaka J. Math. 55 (2018), 315-324; arXiv:1609.07926 [math.NT], 2016.
%t A359651 Select[Range[111,175],Length[Select[IntegerDigits[#],Positive]]==3&&Mod[#,10]!=0 &] (* _Stefano Spezia_, Jan 15 2023 *)
%o A359651 (PARI) list(lim)=my(v=List()); for(d=3, #Str(lim\=1), my(A=10^(d-1)); forstep(a=A, 9*A, A, for(i=1, d-2, my(B=10^i); forstep(b=a+B, a+9*B, B, for(n=b+1, b+9, if(n>lim, return(Vec(v))); listput(v, n)))))); Vec(v)
%Y A359651 Cf. A359098.
%K A359651 nonn,base,easy
%O A359651 1,1
%A A359651 _Charles R Greathouse IV_, Jan 09 2023