A207830 Positive multiples of 3 that contain the decimal digit 1.

12, 15, 18, 21, 51, 81, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 210, 213, 216, 219, 231, 261, 291, 312, 315, 318, 321, 351, 381, 411, 414

Offset

1,1

Comments

I came across this sequence while working some problems in ALCUMUS from the AoPS site. [Tyler]

A 10-automatic set: members are numbers with decimal expansions matching a regular expression. - Charles R Greathouse IV, Feb 20 2012

References

MathCounts 2006 National Target #5

Links

Table of n, a(n) for n=1..55.

Index entries for 10-automatic sequences.

Formula

a(n) = n/3 + O(n^k) where k = log 9/log 10 = 0.954.... - Charles R Greathouse IV, Nov 25 2024

Mathematica

Select[3*Range[138], DigitCount[#, 10, 1] > 0 &] (* Alonso del Arte, Feb 20 2012 *)

Prog

(PARI) is(n)=if(n%3, return(0)); n=vecsort(eval(Vec(Str(n))), , 8); n[1]==1||(#n>1&&n[2]==1) \\ Charles R Greathouse IV, Feb 20 2012
(PARI) is(n)=n%3==0 && setsearch(Set(digits(n)), 1) \\ Charles R Greathouse IV, Feb 12 2017

Crossrefs

Sequence in context: A265128 A243021 A164782 * A348788 A101171 A329731

Adjacent sequences: A207827 A207828 A207829 * A207831 A207832 A207833

Keyword

nonn,base,easy,changed

Author

Seth Tyler, Feb 20 2012

Extensions

a(7)-a(55) from Charles R Greathouse IV, Feb 20 2012

Status

approved