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A125180
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a(n) = 2*a(n-1) + prime(n) - prime(n-1), a(1)=2, where prime(n) denotes the n-th prime.
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3
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2, 5, 12, 26, 56, 114, 232, 466, 936, 1878, 3758, 7522, 15048, 30098, 60200, 120406, 240818, 481638, 963282, 1926568, 3853138, 7706282, 15412568, 30825142, 61650292, 123300588, 246601178, 493202360, 986404722, 1972809448, 3945618910
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OFFSET
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1,1
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COMMENTS
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Limit_{n->oo} a(n)/a(n-1) = 2.
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LINKS
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FORMULA
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a(n) = prime(n) + Sum_{j=1..n-1} 2^(n-j-1)*prime(j), where prime(k) denotes the k-th prime.
a(1) = 2 and a(n) = prime(n) + Sum_{i=1..n-1} a(i) for n > 1. - Alexandre Herrera, Dec 10 2023
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EXAMPLE
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a(4)=26 because 4*prime(1)+2*prime(2)+prime(3)+prime(4) = 8+6+5+7 = 26.
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MAPLE
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a[1]:=2: for n from 2 to 35 do a[n]:=2*a[n-1]+ithprime(n)-ithprime(n-1) od: seq(a[n], n=1..35);
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MATHEMATICA
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a[1] = 2; a[n_] := 2*a[n - 1] + Prime[n] - Prime[n - 1]; Table[a[n], {n, 1, 31}] (* James C. McMahon, Dec 10 2023 *)
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PROG
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(Magma) [n eq 1 select 2 else 2*Self(n-1)+NthPrime(n)-NthPrime(n-1):n in [1..31]]; // Marius A. Burtea, Oct 17 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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