

A271639


Orphans: integers without ancestors, in the sense explained below.


3



648, 649, 659, 737, 738, 739, 747, 748, 749, 758, 759, 769, 828, 829, 837, 838, 839, 846, 847, 848, 849, 857, 858, 859, 868, 869, 879, 919, 928, 929, 937, 938, 939, 946, 947, 948, 949, 956, 957, 958, 959, 967, 968, 969, 978, 979, 989
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OFFSET

1,1


COMMENTS

Look at
2.0.1.6
.2.1.5
We see that 2016 produces 215 if we consider the successive absolute differences of 2016's digits. We call 2016 an "ancestor" of 215. Some integers have many ancestors  215 has 28, for example  and some, the "orphans", have none. The smallest is 648, which is therefore the initial term.
If n is in the sequence, then so are all numbers that start or end with n or are obtained from n by inserting zeros.  Robert Israel, May 27 2019
Eventually almost all numbers are orphans, because there are some impossible substrings, like 919, and any number containing the bad substring is also an orphan. And the fraction of numbers containing any single substring rises asymptotically to 1 (albeit usually slowly).  Allan C. Wechsler, Oct 31 2019.


LINKS



MAPLE

filter:= proc(n) local t, L, i;
L:= convert(n, base, 10);
t:= {$1..9};
for i from 1 to nops(L) do
t:= select(d > d >= 0 and d <= 9, map(d > (d+L[i], dL[i]), t));
if t = {} then return true fi
od;
false
end proc:


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



