

A359925


Numbers with easy multiplication table  the first 9 multiples of these numbers can be derived by either incrementing or decrementing the corresponding digits from the previous multiple.


1



1, 9, 11, 89, 91, 109, 111, 889, 891, 909, 911, 1089, 1091, 1109, 1111, 8889, 8891, 8909, 8911, 9089, 9091, 9109, 9111, 10889, 10891, 10909, 10911, 11089, 11091, 11109, 11111, 88889, 88891, 88909, 88911, 89089, 89091, 89109, 89111, 90889, 90891, 90909, 90911
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OFFSET

1,2


COMMENTS

This is also the list of numbers having exactly one dot or one antidot in each box in the Decimal Exploding Dots notation.


LINKS



FORMULA

a(n) = 10*a(floor(n/2))+2*(n mod 2)1 for n>0, a(0)=0.  Alois P. Heinz, Jan 25 2023


EXAMPLE

a(4) = 89. The first nine multiples of 89 are {089, 178, 267, 356, 445, 534, 623, 712, 801}. The digits in the hundreds place increment by 1, while the digits in the tens and units place decrement by 1. In the Decimal Exploding Dots notation, 89 is represented as DOTANTIDOTANTIDOT = 100  10  1 = 89


MAPLE

a:= proc(n) option remember;
`if`(n=0, 0, 10*a(iquo(n, 2, 'm'))+2*m1)
end:


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



