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

1,2

Links

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

Example

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.

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 *)

Prog

(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, ", ")))

Crossrefs

Cf. A229621, A066568.

Sequence in context: A165250 A257512 A125689 * A230356 A100992 A256382

Adjacent sequences: A244570 A244571 A244572 * A244574 A244575 A244576

Keyword

nonn,base

Author

Derek Orr, Jun 30 2014

Status

approved