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A359651
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Numbers with exactly three nonzero decimal digits and not ending with 0.
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1
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111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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(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.
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LINKS
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MATHEMATICA
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Select[Range[111, 175], Length[Select[IntegerDigits[#], Positive]]==3&&Mod[#, 10]!=0 &] (* Stefano Spezia, Jan 15 2023 *)
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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