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A228730 Lexicographically earliest sequence of distinct nonnegative integers such that the sum of two consecutive terms is a palindrome in base 10.

%I A228730 #34 Nov 08 2022 01:41:26
%S A228730 0,1,2,3,4,5,6,16,17,27,28,38,39,49,50,51,15,7,26,18,37,29,48,40,59,
%T A228730 42,13,9,24,20,35,31,46,53,58,8,14,19,25,30,36,41,47,52,69,32,12,10,
%U A228730 23,21,34,43,45,54,57,44,11,22,33,55,56,65,66,75,76,85,86,95,96
%N A228730 Lexicographically earliest sequence of distinct nonnegative integers such that the sum of two consecutive terms is a palindrome in base 10.
%C A228730 From _M. F. Hasler_, Nov 09 2013: (Start)
%C A228730 At each step, choose the smallest number not occurring earlier and such that a(n+1)+a(n) are palindromes, for all n.
%C A228730 Conjectured to be a permutation of the nonnegative integers.
%C A228730 See A062932 where injectivity is replaced by monotonicity; the sequences differ from a(16)=15 on.
%C A228730 This is an "arithmetic" analog to sequences A228407 and A228410, where instead of the sum, the union of the digits of subsequent terms is considered. (End)
%H A228730 Paul Tek, <a href="/A228730/b228730.txt">Table of n, a(n) for n = 0..10000</a> (corrected by Michel Marcus, Jan 19 2019)
%H A228730 Paul Tek, <a href="/A228730/a228730.txt">PERL program for this sequence</a>
%e A228730 a(1) + a(2) = 3.
%e A228730 a(2) + a(3) = 5.
%e A228730 a(3) + a(4) = 7.
%e A228730 a(4) + a(5) = 9.
%e A228730 a(5) + a(6) = 11.
%e A228730 a(6) + a(7) = 22.
%e A228730 a(7) + a(8) = 33.
%o A228730 (Perl) See Link section.
%o A228730 (PARI) {a=0;u=0; for(n=1, 99, u+=1<<a; print1(a", "); for(k=1, 9e9, !bittest(u, k)&&is_A002113(a+k)&&(a=k)&&next(2)))} \\ _M. F. Hasler_, Nov 09 2013
%o A228730 (Python)
%o A228730 from itertools import islice
%o A228730 def ispal(n): s = str(n); return s == s[::-1]
%o A228730 def agen(): # generator of terms
%o A228730     aset, an, mink = {0}, 0, 1
%o A228730     yield 0
%o A228730     while True:
%o A228730         k = mink
%o A228730         while k in aset or not ispal(an + k): k += 1
%o A228730         an = k; aset.add(an); yield an
%o A228730         while mink in aset: mink += 1
%o A228730 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Nov 07 2022
%Y A228730 Cf. A002113, A055266.
%Y A228730 Cf. A062932 (strictly increasing variant).
%K A228730 nonn,base
%O A228730 0,3
%A A228730 _Paul Tek_, Aug 31 2013
%E A228730 a(0)=0 added by _M. F. Hasler_, Nov 15 2013