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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 Robert Israel, Table of n, a(n) for n = 1..10000 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 Adjacent sequences: A271636 A271637 A271638 * A271640 A271641 A271642 KEYWORD nonn,base AUTHOR Eric Angelini and Jean-Marc Falcoz, Apr 11 2016 STATUS approved

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