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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 (list; graph; refs; listen; history; text; internal format)
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
Global Math Week, Exploding Dots.
Gevorg Hmayakyan, Generalizing a Trig Identity [mentions this sequence]
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
a(n) = 2*A256290(n-1) + 1 for n>1. - Hugo Pfoertner, Jan 28 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 DOT-ANTIDOT-ANTIDOT = 100 - 10 - 1 = 89
MAPLE
a:= proc(n) option remember;
`if`(n=0, 0, 10*a(iquo(n, 2, 'm'))+2*m-1)
end:
seq(a(n), n=1..44); # Alois P. Heinz, Jan 25 2023
CROSSREFS
Column k=10 of A360099.
Sequence in context: A195992 A108687 A038301 * A277998 A289288 A137016
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified June 7 20:32 EDT 2023. Contains 363157 sequences. (Running on oeis4.)