cp's OEIS Frontend

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.

%I A359925 #46 Jan 30 2023 18:49:55
%S A359925 1,9,11,89,91,109,111,889,891,909,911,1089,1091,1109,1111,8889,8891,
%T A359925 8909,8911,9089,9091,9109,9111,10889,10891,10909,10911,11089,11091,
%U A359925 11109,11111,88889,88891,88909,88911,89089,89091,89109,89111,90889,90891,90909,90911
%N 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.
%C A359925 This is also the list of numbers having exactly one dot or one antidot in each box in the Decimal Exploding Dots notation.
%H A359925 Global Math Week, <a href="https://www.explodingdots.org">Exploding Dots</a>.
%H A359925 Gevorg Hmayakyan, <a href="http://math.stackexchange.com/questions/1918281/generalizing-a-trig-identity">Generalizing a Trig Identity</a> [mentions this sequence]
%F A359925 a(n) = 10*a(floor(n/2))+2*(n mod 2)-1 for n>0, a(0)=0. - _Alois P. Heinz_, Jan 25 2023
%F A359925 a(n) = 2*A256290(n-1) + 1 for n>1. - _Hugo Pfoertner_, Jan 28 2023
%e A359925 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
%p A359925 a:= proc(n) option remember;
%p A359925       `if`(n=0, 0, 10*a(iquo(n, 2, 'm'))+2*m-1)
%p A359925     end:
%p A359925 seq(a(n), n=1..44);   # _Alois P. Heinz_, Jan 25 2023
%Y A359925 Cf. A006257, A147991, A147992, A153777, A147993, A256290.
%Y A359925 Column k=10 of A360099.
%K A359925 nonn,base
%O A359925 1,2
%A A359925 _Kiran Ananthpur Bacche_, Jan 25 2023