cp's OEIS Frontend

A261678 Even numbers that are not the sum of two binary palindromes.

%I A261678 #36 Aug 03 2017 04:57:38
%S A261678 176,188,208,242,244,310,524,628,656,736,754,794,832,862,866,868,880,
%T A261678 932,944,994,1000,1180,1240,1308,1310,1328,1342,1352,1376,1408,1420,
%U A261678 1432,1440,1810,1890,1922,1946,1954,2126,2206,2228,2262,2456,2468,2498,2500
%N A261678 Even numbers that are not the sum of two binary palindromes.
%C A261678 Even numbers that are not the sum of two terms from A006995.
%C A261678 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 A261678 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 A261678 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 A261678 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 A261678 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 A261678 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 A261678 lim = 2502; Complement[Most[2 Range@(lim/2)], TakeWhile[DeleteDuplicates@
%t A261678 Sort[Total /@ Tuples[Select[Range@ lim, palQ[#, 2] &], 2]], # < lim &]] (* _Michael De Vlieger_, Sep 14 2015 *)
%Y A261678 Cf. A006995, A241491 (this sequence divided by 2).
%K A261678 nonn,base
%O A261678 1,1
%A A261678 _N. J. A. Sloane_, Sep 04 2015