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First differences of A004125.
13

%I #15 Sep 14 2024 06:51:34

%S 0,1,0,3,-1,5,0,4,1,9,-5,11,3,5,0,15,-4,17,-3,9,7,21,-13,18,9,13,-1,

%T 27,-13,29,0,17,13,21,-20,35,15,21,-11,39,-13,41,3,11,19,45,-29,40,6,

%U 29,5,51,-13,37,-9,33,25,57,-49,59,27,21,0,45,-13,65,9,41,-5,69,-52,71,33,25,11,57,-13,77,-27,40,37,81,-57,61,39,53,-5

%N First differences of A004125.

%C It appears that (1) a(n)=0 if and only if n is a power of 2 and (2) a(n)=n-1 if and only if n+1 is a prime. (This has been verified for the first 2000 terms.)

%H Reinhard Zumkeller, <a href="/A120444/b120444.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A005408(n) - A000203(n+1). - _Omar E. Pol_, Jan 24 2014

%o (Haskell)

%o a120444 n = a120444_list !! (n-1)

%o a120444_list = zipWith (-) (tail a004125_list) a004125_list

%o -- _Reinhard Zumkeller_, May 30 2015

%Y Cf. A000203, A004125, A005408.

%K sign,easy

%O 1,4

%A _John W. Layman_, Jul 19 2006