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A131835
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Numbers starting with 1.
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26
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1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142
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listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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The lower and upper asymptotic densities of this sequence are 1/9 and 5/9, respectively. - Amiram Eldar, Feb 27 2021
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LINKS
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Bryan Brown, Michael Dairyko, Stephan Ramon Garcia, Bob Lutz and Michael Someck, Four quotient set gems, The American Mathematical Monthly, Vol. 121, No. 7 (2014), pp. 590-598; arXiv preprint, arXiv:1312.1036 [math.NT], 2013.
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FORMULA
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MAPLE
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isA131835 := proc(n) if op(-1, convert(n, base, 10)) = 1 then true; else false ; fi ; end: for n from 1 to 300 do if isA131835(n) then printf("%d, ", n) ; fi ; od : # R. J. Mathar, Jul 24 2007
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MATHEMATICA
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Select[Range[150], IntegerDigits[#][[1]] == 1 &] (* Amiram Eldar, Feb 27 2021 *)
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PROG
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(Haskell)
a131835 n = a131835_list !! (n-1)
a131835_list = concat $
iterate (concatMap (\x -> map (+ 10 * x) [0..9])) [1]
(PARI) a(n, {base=10}) = my (o=1); while (n>o, n-=o; o*=base); return (o+n-1) \\ Rémy Sigrist, Jun 23 2017
(PARI) a(n) = n--; s = #digits(9*n+1); n + 8 * (10^(s-1))/9 + 1/9 \\ David A. Corneth, Jun 23 2017
(PARI) nxt(n) = my(d = digits(n+1)); if(d[1]==1, n+1, 10^#d) \\ David A. Corneth, Jun 23 2017
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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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Andrew Good (yipes_stripes(AT)yahoo.com), Jul 20 2007
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EXTENSIONS
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STATUS
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approved
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