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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 (list; graph; refs; listen; history; text; internal format)
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.
Also numbers that do not appear in A040115. - Rémy Sigrist, Jun 10 2017
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], d-L[i]), t));
if t = {} then return true fi
od;
false
end proc:
select(filter, [$1..2000]); # Robert Israel, May 27 2019
CROSSREFS
Cf. A040115.
Sequence in context: A035885 A114827 A334896 * A034281 A157432 A272780
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified April 23 06:45 EDT 2024. Contains 371906 sequences. (Running on oeis4.)