The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A189639 Numbers n such that n'' = n'+1 where n' and n'' are respectively the first and the second arithmetic derivative of n (A003415). 3
161, 209, 221, 1935, 4265, 15941, 22217, 24041, 25637, 30377, 38117, 39077, 48617, 49097, 55877, 68441, 73817, 76457, 80357, 88457, 95237, 98117, 99941, 105641, 110057, 115397, 122537, 130217, 131141, 136517, 143237, 147941, 148697, 152357, 154457, 159077 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The arithmetic derivative of a(n) is a Giuga's number A007850 (solution of n' = n+1).
LINKS
Reinhard Zumkeller and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 100 terms from Reinhard Zumkeller)
EXAMPLE
161' = 30, 161'' = 30' = 31 ==> 161'' = 161'+1 so 161 is a term.
PROG
(PARI) /* using Michael B. Porter's code from A003415: */
A003415(n) = {local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))} /* arithmetic derivative */
for(n=1, 10^6, d1=A003415(n); d2=A003415(d1); if(d2==d1+1, print1(n, ", "))); /* show terms */
/* Joerg Arndt, Apr 25 2011 */
(Haskell)
import Data.List (elemIndices)
a189710 n = a189710_list !! (n-1)
a189710_list = elemIndices 0 $
zipWith (-) (map a003415 a003415_list) (map pred a003415_list)
-- Reinhard Zumkeller, May 09 2011
CROSSREFS
Sequence in context: A025350 A025342 A371338 * A348426 A298615 A250644
KEYWORD
nonn,look
AUTHOR
Giorgio Balzarotti, Apr 24 2011
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 20:03 EDT 2024. Contains 373464 sequences. (Running on oeis4.)