A261678 - OEIS

%I #36 Aug 03 2017 04:57:38

%S 176,188,208,242,244,310,524,628,656,736,754,794,832,862,866,868,880,

%T 932,944,994,1000,1180,1240,1308,1310,1328,1342,1352,1376,1408,1420,

%U 1432,1440,1810,1890,1922,1946,1954,2126,2206,2228,2262,2456,2468,2498,2500

%N Even numbers that are not the sum of two binary palindromes.

%C Even numbers that are not the sum of two terms from A006995.

%C A subsequence of the numbers that are not the sum of three terms from A006995. The two sequences are equal if every odd number is the sum of three terms from A006995 (which is equivalent to the conjecture in A261680). - _Chai Wah Wu_, Sep 14 2015

%H N. J. A. Sloane, <a href="/A261678/b261678.txt">Table of n, a(n) for n = 1..10000</a> [Based on Robert Israel's b-file for A241491]

%H Aayush Rajasekaran, Jeffrey Shallit, and Tim Smith, <a href="https://arxiv.org/abs/1706.10206">Sums of Palindromes: an Approach via Nested-Word Automata</a>, preprint arXiv:1706.10206 [cs.FL], June 30 2017.

%p R:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:

%p P:=proc(q) local a,b,k,n,ok; n:=2*q; ok:=1; for k from 1 to trunc(n/2) do a:=convert(k,binary,decimal); b:=convert(n-k,binary,decimal);

%p if a=R(a) and b=R(b) then ok:=0; break; fi; od; if ok=1 then n; fi; end: seq(P(i),i=1..1250); # _Paolo P. Lava_, Aug 03 2017

%t lim = 2502; Complement[Most[2 Range@(lim/2)], TakeWhile[DeleteDuplicates@

%t Sort[Total /@ Tuples[Select[Range@ lim, palQ[#, 2] &], 2]], # < lim &]] (* _Michael De Vlieger_, Sep 14 2015 *)

%Y Cf. A006995, A241491 (this sequence divided by 2).

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Sep 04 2015