A083463 a(n) = smallest number k such that 2^n + k is a palindrome.

0, 0, 0, 0, 6, 1, 2, 3, 6, 3, 87, 64, 18, 36, 77, 55, 20, 59, 118, 137, 825, 750, 610, 230, 545, 1101, 2312, 4703, 9406, 7723, 31877, 73764, 27628, 65266, 27987, 56975, 15050, 981259, 971528, 844057, 532125, 954360, 897830, 884770, 2085155, 5259321

Offset

0,5

Links

Robert Israel, Table of n, a(n) for n = 0..6613

Formula

a(n) = A052036(2^n). - David Wasserman, Nov 11 2004

Example

a(9) = 3 as 2^9 = 512, 512 +3 = 515 is a palindrome.

Maple

rev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
f:= proc(n) local d, e, x, y;
  d:= ilog10(n)+1;
  e:= floor(d/2);
  x:= floor(n/10^e);
  if d::even then
    y:= x*10^e + rev(x);
    if y >= n then y - n else (x+1)*10^e + rev(x+1) - n fi;
   else
    y:= x*10^e + rev(floor(x/10));
    if y >= n then y - n else (x+1)*10^e + rev(floor((x+1)/10)) - n fi
 fi;
end proc:
map(f, [seq(2^n, n=0..50)]); # Robert Israel, Feb 17 2026

Crossrefs

Sequence in context: A089128 A222215 A106687 * A187110 A378994 A013672

Adjacent sequences: A083460 A083461 A083462 * A083464 A083465 A083466

Keyword

base,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 01 2003

Extensions

More terms from David Wasserman, Nov 11 2004

Status

approved