A082208 Palindromes for which the sum of the digits is also a palindrome.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 101, 111, 121, 131, 141, 151, 161, 171, 191, 202, 212, 222, 232, 242, 252, 272, 303, 313, 323, 333, 353, 404, 414, 434, 515, 787, 868, 949, 1001, 1111, 1221, 1331, 2002, 2112, 2222, 2992, 3003, 3113, 3883, 4004

Offset: 1

Author

Amarnath Murthy, Apr 10 2003

Keywords

• base
• nonn

Examples

			4774 is in the sequence because (1) it is a palindrome and (2) the sum of its digits 4 + 7 + 7 + 4 = 22 is also a palindrome.
		

Crossrefs

Cf. A002113, A082207.

Programs

Maple

rev := proc (n) local nn; nn := convert(n, base, 10): add(nn[j]*10^(nops(nn)-j), j = 1 .. nops(nn)) end proc: sd := proc (n) options operator, arrow: add(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: a := proc (n) if rev(n) = n and rev(sd(n)) = sd(n) then n else end if end proc: seq(a(n), n = 0 .. 5000); # Emeric Deutsch, Jan 18 2009

Mathematica

d[n_]:=IntegerDigits[n]; sod[n_]:=Total[d[n]]; palQ[n_]:=Reverse[x=d[n]]==x; t={}; Do[If[palQ[n] && palQ[sod[n]],AppendTo[t,n]],{n,0,4005}]; t (* Jayanta Basu, May 15 2013 *)

Python

from itertools import chain, count, islice
def A082208_gen(): # generator of terms
    return filter(lambda n:(s:=str(sum(int(d) for d in str(n))))[:(t:=(len(s)+1)//2)]==s[:-t-1:-1],chain((0,),chain.from_iterable(chain((int((s:=str(d))+s[-2::-1]) for d in range(10**l,10**(l+1))), (int((s:=str(d))+s[::-1]) for d in range(10**l,10**(l+1)))) for l in count(0))))
A082208_list = list(islice(A082208_gen(),20)) # Chai Wah Wu, Jun 23 2022

Extensions

More terms from Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006; corrected Apr 18 2006; corrected Apr 20 2006

Edited by N. J. A. Sloane, Jan 14 2009 at the suggestion of Ian Kent