A244573 Numbers n such that 10*n + d - digsum(10*n + d) is a palindrome for any d in {0,1,2,3,4,5,6,7,8,9}.

1, 10, 18, 26, 34, 42, 68, 76, 84, 92, 100, 279, 368, 457, 546, 635, 724, 813, 902, 1000, 1071, 1152, 1233, 1314, 1486, 1567, 1648, 1729, 1981, 2051, 2132, 2213, 2385, 2466, 2547, 2628, 2709, 2880, 2961, 3031, 3112, 3284, 3365, 3446, 3527, 3608, 3699, 3860, 3941, 4011, 4183, 4264

Offset: 1

Author

Derek Orr, Jun 30 2014

Keywords

• nonn
• base

Examples

			180 - (1+8+0) = 171, a palindrome. By adding {1,2,3,4,5,6,7,8,9} to 180 and subtracting that number's digsum, it will still be 171, a palindrome. Since 180 = 18*10, 18 is a member of this sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A229621, A066568.

Programs

Mathematica

palQ[n_]:=AnyTrue[Table[10n+d-Total[IntegerDigits[10n+d]],{d,0,9}],PalindromeQ]; Select[Range[4300],palQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 13 2021 *)

PARI

rev(n)={r="";for(i=1,#digits(n),r=concat(Str(digits(n)[i]),r));return(eval(r))}
for(n=1,10^4,s=sum(i=1,#digits(10*n),digits(10*n)[i]);if(rev(10*n-s)==10*n-s,print1(n,", ")))