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

1,1

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.

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 *)

Crossrefs

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

Sequence in context: A172685 A344280 A266058 * A136603 A114824 A370251

Adjacent sequences: A261675 A261676 A261677 * A261679 A261680 A261681

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 04 2015

Status

approved