A084034 - OEIS

%I #38 Oct 10 2018 10:14:28

%S 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,

%T 33,35,36,40,42,44,45,48,49,50,54,55,56,60,63,64,66,70,72,75,77,80,81,

%U 84,88,90,96,98,99,100,105,108,110,111,112,120,121,125,126,128

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

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

%C 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

%C From _David A. Corneth_, Aug 03 2017: (Start)

%C Closed under multiplication.

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

%H David A. Corneth, <a href="/A084034/b084034.txt">Table of n, a(n) for n = 1..12917</a> (Terms <= 10^8)

%e 99 is a member since 99 = 3*33.

%e 9768 is a member since 9768= 2*22*222.

%e 111*2*33*44 = 322344 is a member.

%p 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

%Y Cf. A002275, A010785, A051038, A084348.

%Y A002473 gives products of single-digit numbers.

%K base,nonn

%O 1,3

%A _Amarnath Murthy_, May 26 2003

%E Corrected and extended by _David Wasserman_, Dec 09 2004

%E Corrected data, offset changed to 1 by _David A. Corneth_, Aug 03 2017

%E Edited by _N. J. A. Sloane_, Jul 02 2017 and Oct 10 2018