A052037 Smallest positive number that must be added to n to reach a palindrome.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3

Offset

0,10

Comments

The pattern breaks down as for instance 99 need be added only with 2 instead of 11.

More precisely, the pattern changes (shape and length) at n=9, n=99, n=999, etc. - M. F. Hasler, Apr 26 2014

Links

Robert Israel, Table of n, a(n) for n = 0..10000

P. De Geest, World!Of Numbers

Maple

N:= 3: # to get a(0)..a(10^N)
revdigs:= proc(n) local L, j, nL;
  L:= convert(n, base, 10); nL:= nops(L);
  add(L[j]*10^(nL-j), j=1..nL);
end proc:
palis:= $0..9:
for d from 2 to N do
  if d::even then
    palis:= palis, seq(x*10^(d/2)+revdigs(x), x=10^(d/2-1)..10^(d/2)-1)
  else
    palis:= palis, seq(seq(x*10^((d+1)/2)+y*10^((d-1)/2)+revdigs(x), y=0..9), x=10^((d-3)/2)..10^((d-1)/2)-1);
  fi
od:
palis:= [palis, (10^(N+1)-1)/9]:
f:= proc(n) local k;
  k:= ListTools[BinaryPlace](palis, n);
  if palis[k+1]=n then palis[k+2]-n else palis[k+1]-n fi
end proc:
map(f, [$0..10^N]); # Robert Israel, Jan 08 2018

Mathematica

spn[n_]:=Module[{k=1}, While[!PalindromeQ[n+k], k++]; k]; Join[{1}, Array[spn, 100]] (* Harvey P. Dale, Mar 01 2023 *)

Prog

(PARI) a(n)=for(k=1, 9e19, is_A002113(n+k)&&return(k)) \\ For illustrative purpose only, inefficient for most large numbers. - M. F. Hasler, Apr 26 2014

Crossrefs

Cf. A052036, A002113, A088997.

Sequence in context: A141482 A262144 A079795 * A213302 A308846 A038586

Adjacent sequences: A052034 A052035 A052036 * A052038 A052039 A052040

Keyword

nonn,base,easy

Author

Patrick De Geest, Dec 15 1999

Extensions

Edited by N. J. A. Sloane, Jan 17 2009 at the suggestion of R. J. Mathar

Status

approved