A084034 Numbers which are a product of repeated-digit numbers A010785.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 105, 108, 110, 111, 112, 120, 121, 125, 126, 128

Offset

1,3

Comments

Numbers which can be written as a*b*c*... where a, b, c are numbers whose decimal expansions are repetitions of a single digit.

Superset of A051038. The first numbers in this sequence but not in A051038 are 111, 222, 333, 444, 555. - R. J. Mathar, Sep 17 2008

From David A. Corneth, Aug 03 2017: (Start)

Closed under multiplication.

Multiples of 1-digit primes and numbers of the form (10^n - 1) / 9. (End)

Links

David A. Corneth, Table of n, a(n) for n = 1..12917 (Terms <= 10^8)

Example

99 is a member since 99 = 3*33.
9768 is a member since 9768= 2*22*222.
111*2*33*44 = 322344 is a member.

Maple

isA010786 := proc(n) if nops(convert(convert(n, base, 10), set)) = 1 then true; else false ; fi; end: isA084034 := proc(n, a010785) local d ; if n = 1 then RETURN(true) ; fi; for d in ( numtheory[divisors](n) minus{1} ) do if d in a010785 then if isA084034(n/d, a010785) then RETURN(true) ; fi; fi; od: RETURN(false) ; end: nmax := 1000: a010785 := [] : for k from 1 to nmax do if isA010786(k) then a010785 := [op(a010785), k] ; fi; od: for n from 1 to nmax do if isA084034(n, a010785) then printf("%d, ", n) ; fi; end: # R. J. Mathar, Sep 17 2008

Crossrefs

Cf. A002275, A010785, A051038, A084348.

A002473 gives products of single-digit numbers.

Sequence in context: A033892 A033620 A033637 * A084347 A051038 A140332

Adjacent sequences: A084031 A084032 A084033 * A084035 A084036 A084037

Keyword

base,nonn

Author

Amarnath Murthy, May 26 2003

Extensions

Corrected and extended by David Wasserman, Dec 09 2004

Corrected data, offset changed to 1 by David A. Corneth, Aug 03 2017

Edited by N. J. A. Sloane, Jul 02 2017 and Oct 10 2018

Status

approved