Template:Sequence of the Day for March 30

Intended for: March 30, 2012

Timetable

• First draft to be entered by December 30, 2011
• Draft to be reviewed by January 30, 2012
• Draft to be approved by February 29, 2012

Yesterday's SOTD * Tomorrow's SOTD

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A121023: Multiples of 3 containing a 3 in their decimal representation.

{ 3, 30, 33, 36, 39, 63, 93, 123, 132, 135, 138, 153, 183, 213, 231, ... }

The graph of this sequence is (roughly) self-similar: it has the same appearance when the scale is multiplied by 10.

The same can be generalized to multiples of any other number

d

which have

d

as a substring in their decimal (or other?) expansion. Sequences A011531 (numbers having the digit 1) and A121022 through A121040 cover this for

d

= 1, ..., 20.

Another generalization is that of numbers containing some or all of their divisors as substrings in their decimal expansion, or simply the digits thereof. Relevant sequences include

• A092911: All divisors can be formed using the digits of the number.
• A239058: All divisors are a substring of the decimal expansion, which is the union of primes having a digit 1 (A208270).

and the more challenging

• A239060: Non-prime numbers having all divisors are a substring of the decimal expansion. (Of which the 4th term is not yet known!)