login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033665 Number of 'Reverse and Add' steps needed to reach a palindrome starting at n, or -1 if n never reaches a palindrome. 17
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 1, 1, 1, 1, 2, 1, 0, 2, 3, 4, 1, 1, 1, 2, 1, 2, 2, 0, 4, 6, 1, 1, 2, 1, 2, 2, 3, 4, 0, 24, 1, 2, 1, 2, 2, 3, 4, 6, 24, 0, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,20

COMMENTS

Palindromes themselves are not 'Reverse and Add!'ed, so they yield a zero!

REFERENCES

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 142-3 Penguin Books 1987.

LINKS

Kerry Mitchell, Table of n, a(n) for n = 0..195

P. De Geest, Some thematic websources

Jason Doucette, World Records

S. K. Eddins, The Palindromic Order Of A Number

Kerry Mitchell, Table of n, a(n) for n = 0..10000 (The -1 entries are only conjectural)

Kerry Mitchell, Table of n, a(n) for n = 0..100000 (The -1 entries are only conjectural)

I. Peter, More trajectories

T. Trotter, Jr., Palindrome Power

Index entries for sequences related to Reverse and Add!

EXAMPLE

19 -> 19+91 = 110 -> 110+011 = 121 = palindrome, took 2 steps, so a(19)=2.

MATHEMATICA

rev[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; radd[n_]:=n+rev[n];

pal[n_]:=If[n==rev[n], True, False];

raddN[n_]:=Length[NestWhileList[radd[#]&, n, pal[#]==False&]]-1;

raddN/@Range[0, 195] (* Ivan N. Ianakiev, Aug 31 2015 *)

PROG

(PARI)

rev(n)={d=digits(n); p=""; for(i=1, #d, p=concat(Str(d[i]), p)); return(eval(p))}

a(n)=if(n==rev(n), return(0)); for(k=1, 10^3, i=n+rev(n); if(rev(i)==i, return(k)); n=i)

n=0; while(n<100, print1(a(n), ", "); n++) \\ Derek Orr, Jul 28 2014

CROSSREFS

Cf. A023108, A023109, A006960, A016016, A063048.

Equals A030547(n) - 1.

Sequence in context: A236747 A194285 A135341 * A104234 A037870 A250205

Adjacent sequences:  A033662 A033663 A033664 * A033666 A033667 A033668

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Patrick De Geest, Jun 15 1998

I truncated the b-file at n=195, since the value of a(196) is not presently known (cf. A006960). The old b-files are now a-files. - N. J. A. Sloane, May 09 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 19 16:10 EST 2017. Contains 294936 sequences.