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!)
A165135 The number of n-digit positive papaya numbers. 6
9, 90, 252, 1872, 4464, 29250, 62946, 393912, 809442, 4945140, 9899910, 59366286, 116999892, 692936460, 1349989992, 7919601912, 15299999856, 89099130960, 170999999838, 989995038012, 1889999872488, 10889990099100, 20699999999802, 118799939782206, 224999999981964 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Papaya numbers are concatenations of two palindromes or palindromes themselves. All one-digit and two-digit numbers are papaya numbers.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Tanya Khovanova, Papaya Words and Numbers

FORMULA

a(n) = A052268(n)-A165611(n). - R. J. Mathar, Sep 25 2009

a(n) = 9*R(n,10)/10 - Sum_{d|n,d<n} phi(n/d)*a(d) where R(2*k,r)=k*(r+1)*r^k, R(2*k+1,r)=(2*k+1)*r^(k+1). - Andrew Howroyd, Mar 29 2016

EXAMPLE

Three-digit papaya numbers are of four types: aaa (total of 9) and aab, aba, abb, (total of 81 for each). Hence a(3) = 252.

PROG

(PARI)

R(n, b)=if(n%2==0, n/2*(b+1)*b^(n/2), n*b^((n+1)/2));

a(n) = 9*R(n, 10)/10 - sumdiv(n, d, if(n<>d, eulerphi(n/d)*a(d))); \\ Andrew Howroyd, Oct 14 2017

CROSSREFS

Cf. A007055, A052268, A165610, A165611.

Sequence in context: A140160 A043960 A044641 * A277105 A180289 A210088

Adjacent sequences:  A165132 A165133 A165134 * A165136 A165137 A165138

KEYWORD

base,nonn

AUTHOR

Sergei Bernstein and Tanya Khovanova, Sep 04 2009

EXTENSIONS

a(7)-a(8) from R. J. Mathar, Sep 25 2009

a(9)-a(25) from Andrew Howroyd, Mar 29 2016

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 December 11 15:43 EST 2017. Contains 295905 sequences.