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%I #7 Mar 18 2020 16:26:08
%S 1,3,7,29,117,1873,7493,119889,479557,7672913,491066433,1964265733,
%T 125713006913,2011408110609,8045632442437,128730119078993,
%U 8238727621055553,527278567747555393,2109114270990221573,134983313343374180673,2159733013493986890769,8638932053975947563077
%N a(0) = 1; thereafter a(n) = 2^(prime(n)-1) + Sum_{k=1..n} 2^(prime(n)-prime(k)).
%F a(n) = floor(c * 2^prime(n)) for n > 0, where c = 0.91468250985... = 1/2 + A051006.
%e a(7) = 119889 (in base 10) = 11101010001010001 (in base 2).
%e ||| | | | | |
%e 123 5 7 1113 17
%t a[0] = 1; a[n_] := 2^(Prime[n] - 1) + Sum[2^(Prime[n] - Prime[k]), {k, 1, n}]; Table[a[n], {n, 0, 21}]
%o (PARI) a(n) = if (n==0, 1, 2^(prime(n)-1) + sum(k=1, n, 2^(prime(n)-prime(k)))); \\ _Michel Marcus_, Mar 18 2020
%Y Cf. A000040, A008578, A010051, A034785, A051006, A072762, A076793, A080339, A080355, A121240, A139104, A333393.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Mar 18 2020