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

176, 188, 208, 242, 244, 310, 524, 628, 656, 736, 754, 794, 832, 862, 866, 868, 880, 932, 944, 994, 1000, 1180, 1240, 1308, 1310, 1328, 1342, 1352, 1376, 1408, 1420, 1432, 1440, 1810, 1890, 1922, 1946, 1954, 2126, 2206, 2228, 2262, 2456, 2468, 2498, 2500

Offset: 1

Author

N. J. A. Sloane, Sep 04 2015

Keywords

• nonn
• base

Comments

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

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

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000 [Based on Robert Israel's b-file for A241491]
• Aayush Rajasekaran, Jeffrey Shallit, and Tim Smith, Sums of Palindromes: an Approach via Nested-Word Automata, preprint arXiv:1706.10206 [cs.FL], June 30 2017.

Crossrefs

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

Programs

Maple

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:=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);
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

Mathematica

lim = 2502; Complement[Most[2 Range@(lim/2)], TakeWhile[DeleteDuplicates@
Sort[Total /@ Tuples[Select[Range@ lim, palQ[#, 2] &], 2]], # < lim &]] (* Michael De Vlieger, Sep 14 2015 *)