A333392 a(0) = 1; thereafter a(n) = 2^(prime(n)-1) + Sum_{k=1..n} 2^(prime(n)-prime(k)).
1, 3, 7, 29, 117, 1873, 7493, 119889, 479557, 7672913, 491066433, 1964265733, 125713006913, 2011408110609, 8045632442437, 128730119078993, 8238727621055553, 527278567747555393, 2109114270990221573, 134983313343374180673, 2159733013493986890769, 8638932053975947563077
Offset: 0
Keywords
Examples
a(7) = 119889 (in base 10) = 11101010001010001 (in base 2).
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123 5 7 1113 17
Crossrefs
Programs
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Mathematica
a[0] = 1; a[n_] := 2^(Prime[n] - 1) + Sum[2^(Prime[n] - Prime[k]), {k, 1, n}]; Table[a[n], {n, 0, 21}] -
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
Formula
a(n) = floor(c * 2^prime(n)) for n > 0, where c = 0.91468250985... = 1/2 + A051006.