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%I #23 Aug 20 2014 22:11:33
%S 2,-2,-10,6,-26,38,-90,166,678,1702,-346,3750,-4442,11942,44710,
%T 110246,-20826,241318,-282970,765606,2862758,7057062,-1331546,
%U 15445670,49000102,116108966,250326694,518762150,-18108762,1055633062
%N Sum_{k=1..n} (-1)^isprime(k)*2^k.
%C Inspired by A243106. In contrast to that sequence, the absolute values are not increasing here.
%C This can be explained as follows: By comparison of the absolute values among both sequences, after replacing for each term at the other sequence: 8,9 with 0,1 it is obtained the a(n) corresponding here expressed in binary with one or more "leading zeros". This induces the described effect, cf. example. - _R. J. Cano_, Aug 20 2014
%H Jens Kruse Andersen, <a href="/A242002/b242002.txt">Table of n, a(n) for n = 1..1000</a>
%e From _R. J. Cano_, Aug 20 2014: (Start)
%e By looking at A243106's b-file for n=28..30:
%e 28 11110911090911090911090908910
%e 29 -88889088909088909088909091090
%e 30 911110911090911090911090908910
%e After taking the absolute values, making the replacements, and deleting the leading zeros, we obtain:
%e 28 11110111010111010111010100110
%e 29 1000101000101000101011010 (4 leading zeros deleted)
%e 30 111110111010111010111010100110
%e From where it is noticeable that abs(a(28))>abs(a(29))<abs(a(30)); Now by reading from binary:
%e abs(a(28))=518762150
%e abs(a(29))=18108762 (it was negative)
%e abs(a(30))=1055633062 (End)
%o (PARI) a(n,b=2)=sum(k=1,n,(-1)^isprime(k)*b^k)
%K sign
%O 1,1
%A _M. F. Hasler_, Aug 20 2014
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