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, 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
Offset: 1
Examples
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
Links
- Global Math Week, Exploding Dots.
- Gevorg Hmayakyan, Generalizing a Trig Identity [mentions this sequence]
Programs
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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
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
Comments