A327270 -id:A327270 - cp's OEIS frontend

A271639 Orphans: integers without ancestors, in the sense explained below.

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, 1648, 1649, 1659, 1737, 1738

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Apr 11 2016

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.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A040115.

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

\\ Needs PARI from A327270.
select(k->A327270(k)<0, [1..1800]) \\ Andrew Howroyd, Dec 10 2024

A086919 Smallest number whose absolute value of the successive digit difference is the n-th palindrome, or -1 if no such number exists.

Original entry on oeis.org

11, 10, 13, 14, 15, 16, 17, 18, 19, 90, 101, 131, 141, 151, 161, 171, 181, 191, 909, 1001, 1010, 1021, 1032, 1043, 1054, 1065, 1076, 1087, 1098, 1331, 1320, 1313, 1302, 1375, 1386, 1397, 2075, 2086, 2097, 1441, 1430, 1425, 1414, 1403, 1496, 3063, 3074, 3085, 3096, 1551

Offset: 1

Amarnath Murthy, Sep 18 2003

Palindromes without solutions are the palindromes in A271639. The first is 737 corresponding to a(83) = -1. - Andrew Howroyd, Dec 10 2024

			The term corresponding to the palindrome 262 is 1397 and the next term (corresponding to 272) is 2075.

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Cf. A002113, A086918, A271639, A327270.

a(n) = A327270(A002113(n)) for n > 1. - Andrew Howroyd, Dec 10 2024

Offset changed and a(37) onwards from Andrew Howroyd, Dec 10 2024

cp's OEIS Frontend

A271639 Orphans: integers without ancestors, in the sense explained below.

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