RE: Operating on every k-th element of list?

• To: mathgroup at smc.vnet.net
• Subject: [mg37092] RE: [mg37080] Operating on every k-th element of list?
• From: "DrBob" <drbob at bigfoot.com>
• Date: Wed, 9 Oct 2002 05:25:42 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Here's a start, with a more complicated function:

lst = Range[50];
f = #1^2 & ;
k = 7;
r = Range[k + 1, Length[lst], k];
lst[[r]] = lst[[r]] + f /@ lst[[r - 1]];
lst

{1, 2, 3, 4, 5, 6, 7, 57, 9, 10, 11, 12, 13, 14, 211, 16, 17, 18, 19,
20, 21, 463, 23, 24, 25, 26, 27, 28, 813, 30, 31, 32, 33, 34, 35, 1261,
37, 38, 39, 40, 41, 42, 1807, 44, 45, 46, 47, 48, 49, 2451}

or:

g[lst_List, k_Integer?Positive, f_Function] := Module[
{result = lst, r = Range[k + 1, Length[lst], k]},
result[[r]] = result[[r]] + f /@ lst[[r - 1]];
result
]
lst = Range[50];
lst = g[lst, 7, #1^2 & ]

or:

lst = Range[50];
lst + Drop[Prepend[MapIndexed[If[Mod[First@#2, k] == 0, f@#1, 0] &,
lst], 0], -1]

DrBob

-----Original Message-----
From: AES [mailto:siegman at stanford.edu]
To: mathgroup at smc.vnet.net
Subject: [mg37092] [mg37080] Operating on every k-th element of list?

I want to apply a function to every  k-th  element of a long list and
add the result to the  k+1  element.

[Actually  k = 3  and I just want to multiply  myList[[k]]  by a
constant (independent of k)  and add the result to  myList[[k+1]]  for
every value of  k  that's divisible by 3.]

Is there a way to do this -- or in general to get at every  k-th
element of a list -- that's faster and more elegant than writing a brute

force  Do[]  loop or using  Mod[]  operators, and that will take
advantage of native List operators,  but still not be too recondite?

I've been thinking about multiplying a copy of  myList  by a "mask list"

{0,0,1,0,0,1,..} to generate a "masked copy" and approaches like that.
Better ways???

```

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