Search: id:A114216
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%I A114216
%S A114216 1,1,3,5,1,7,3,11,17,23,27,1,21,1,3,7,33,47,57,1,37,29,7,3,25,63,83,95,
%T A114216 51,41,21,19,39,89,119,135,73,59,113,143,161,171,181,187,3,101,39,131,
%U A114216 179,51,71,155,99,175,27,145,207,239,129,205,61,177,121,27,85,201,133
%N A114216 Sum of first n primes divided by maximal power of 2, see formula.
%C A114216 a(33899) = 123729 and 33900-th prime is 400559, hence 123729 + 400559 
               = 524288 = 2^19 and a(33900) = 1. Is a(33900) the last term equal 
               to 1? No other terms with n<10000000. Cf. A114217 values of n for 
               which A114216(n)=1 and A114218 values of k for n with A114216(n)=1.
%F A114216 a(n)=(a(n-1)+n-th prime)/2^k with maximal possible k and with a(1)=1.
%e A114216 prime(1)=2 hence a(1)=2/2^2=1; prime(2)=3 hence a(2)=(a(1)+3)/2^2=1; 
               prime(3)=5 hence a(3)=(a(2)+5)/2^1=3; prime(4)=7 hence a(4)=(a(3)+7)/
               2^1=5 etc.
%Y A114216 Cf. A114217, A114218.
%Y A114216 Sequence in context: A133045 A158858 A152204 this_sequence A086233 A065395 
               A112411
%Y A114216 Adjacent sequences: A114213 A114214 A114215 this_sequence A114217 A114218 
               A114219
%K A114216 nonn
%O A114216 1,3
%A A114216 Zak Seidov (zakseidov(AT)yahoo.com), Nov 18 2005

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