90 lines
5.5 KiB
HTML
90 lines
5.5 KiB
HTML
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<h2>Primonacci</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 304</h3><span style="width:300px;color:#666;">Published on Sunday, 3rd October 2010, 01:00 am; Solved by 994</span></div>
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For any positive integer <var>n</var> the function next_prime(<var>n</var>) returns the smallest prime p <BR /> such that p<img src='images/symbol_gt.gif' width='10' height='10' alt='>' border='0' style='vertical-align:middle;' /><var>n</var>.
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The sequence a(<var>n</var>) is defined by:<BR />
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a(1)=next_prime(10<sup>14</sup>) and a(<var>n</var>)=next_prime(a(<var>n</var>-1)) for n<img src='images/symbol_gt.gif' width='10' height='10' alt='>' border='0' style='vertical-align:middle;' />1.
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<p/>
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The fibonacci sequence f(<var>n</var>) is defined by:
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f(0)=0, f(1)=1 and f(<var>n</var>)=f(<var>n</var>-1)+f(<var>n</var>-2) for <var>n</var><img src='images/symbol_gt.gif' width='10' height='10' alt='>' border='0' style='vertical-align:middle;' />1.
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The sequence b(<var>n</var>) is defined as f(a(<var>n</var>)).
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Find <img src='images/symbol_sum.gif' width='11' height='14' alt='∑' border='0' style='vertical-align:middle;' />b(<var>n</var>) for 1<img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /><var>n</var><img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' />100 000.
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Give your answer mod 1234567891011.
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