%I A121497
%S A121497 0,1,4,10,21,41,78,148,282,537,1013,1882,3446,6267,11468,21416,41209,
%T A121497 81771,166042,340994,700570,1429375,2886777,5771828,11453105,22638215,
%U A121497 44742141,88681674,176545766,352992931,707922077,1421120880,2849433326
%N A121497 Binomial transform of the characteristic function of the prime numbers 
               (A010051).
%C A121497 This is the binomial transform of the sequence {0,0,1,1,0,1,0,1,...}. 
               Sequence A052467, the binomial transform of the sequence {0,1,1,0,
               1,0,1,...} is very similar. In fact, the first differences of this 
               sequence yields A052467.
%C A121497 The number of pernicious numbers (A052294) less than 2^n. Although the 
               graph looks almost like 2^n, the graph of a(n)/2^n has quite a bit 
               of variation. - T. D. Noe, Mar 14 2009
%H A121497 T. D. Noe, <a href="b121497.txt">Table of n, a(n) for n=1..1000</a>
%F A121497 a(n)=sum_{i=1..pi(n)} binomial(n,prime(i)), where pi(n) is the number 
               of primes <= n.
%t A121497 Table[Sum[Binomial[n,Prime[i]], {i,PrimePi[n]}], {n,40}]
%Y A121497 Sequence in context: A024988 A144897 A001891 this_sequence A132925 A166553 
               A053643
%Y A121497 Adjacent sequences: A121494 A121495 A121496 this_sequence A121498 A121499 
               A121500
%K A121497 nonn
%O A121497 1,3
%A A121497 T. D. Noe (noe(AT)sspectra.com), Aug 03 2006