A056964 a(n) = n + reversal of digits of n.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 66, 77, 88, 99, 110

Offset: 0

Author

Henry Bottomley, Jul 18 2000

Keywords

• nonn
• base
• easy

Comments

If n has an even number of digits then a(n) is a multiple of 11.

Also called the Reverse and Add!, or RADD operation. Iteration of this function leads to the definition of Lychrel and related numbers, cf. A023108, A063048, A088753, A006960, and many others. - M. F. Hasler, Apr 13 2019

Examples

			a(17) = 17 + 71 = 88.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..20000 (first 1001 terms from T. D. Noe)
• Eric Weisstein's World of Mathematics, Reverse-Then-Add Sequence
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A004086, A056965, A067030.

Differs from A052008 when n=101 and a(101)=202 while A052008(101)=121

Cf. A036839.

Programs

Haskell

a056964 n = n + a004086 n  -- Reinhard Zumkeller, Oct 14 2011

Mathematica

Table[n+FromDigits[Reverse[IntegerDigits[n]]],{n,0,100}] (* Harvey P. Dale, Jul 19 2014 *)
#+IntegerReverse[#]&/@Range[0,100] (* Harvey P. Dale, Jul 31 2025 *)

PARI

A056964(n)=fromdigits(Vecrev(digits(n)))+n \\ Charles R Greathouse IV, Oct 28 2014

Python

def A056964(n): return n+int(str(n)[::-1]) # Indranil Ghosh, Jan 29 2017

Formula

a(n) = n + A004086(n) = 2*n - A056965(n).

n < a(n) < 11n for n > 0. - Charles R Greathouse IV, Nov 17 2022