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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

Cf. A003415, A007850, A054377, A132632, A189639.

Sequence in context: A249397 A025350 A025342 * A298615 A250644 A060641

Adjacent sequences:  A189636 A189637 A189638 * A189640 A189641 A189642

KEYWORD

nonn,look

AUTHOR

Giorgio Balzarotti, Apr 24 2011

STATUS

approved

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Last modified October 16 06:24 EDT 2019. Contains 328049 sequences. (Running on oeis4.)