A136687 Number of palindromes in the range [0,n] inclusive.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 0

Author

N. J. A. Sloane, Apr 21 2008

Keywords

• nonn
• base

Comments

Partial sums of A136522. [Typo fixed by Colin Barker, Apr 26 2015]

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..20202

Crossrefs

Cf. A002113, A136522, A137180, A261423.

Programs

Mathematica

palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; Accumulate[ Table[ If[palQ[n],1,0],{n,0,80}]] (* Harvey P. Dale, May 11 2014 *)

PARI

A136687(n)=inv_A002113(A261423(n)) \\ M. F. Hasler, Sep 09 2018

Python

def A136687(n):
    l = len(s:=str(n))
    k = l+1>>1
    return n//10**(l-k)-(int(s[k-1::-1])>n%10**k)+10**(k-1+(l&1^1)) # Chai Wah Wu, Jul 24 2024

Formula

a(n) = inv_A002113(A261423(n)), where inv_A002113 is the inverse of A002113, i.e., it yields the index of a palindrome. - M. F. Hasler, Sep 10 2018