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A152006
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A Fernandez expansion of the extended primes ( primes plus {0,1}): f(n)=If[n < 2, n, Prime[n - 1]]; p(x,n)=Product[1 + f(m)*x^m, {m, 0, n}];a(n)=coefficients(p(x,n).
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0
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1, 1, 2, 5, 8, 18, 34, 63, 102, 203, 336, 589, 999, 1675, 2799, 4768, 7561, 12224, 20513, 31724, 51621, 81976, 128560, 199192, 312536, 482806, 744847, 1147952, 1755931, 2649474, 4051413, 6069450, 9105323, 13747364, 20335077, 30508629, 45198631
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The n=100 ratio of this extension is:1.3307144309558037. The ordinary definition gives:1.3485468888430188. Maybe I should comment that my Mathematica procedure gives a different result for A147557 than the one in OEIS.
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FORMULA
| f(n)=If[n < 2, n, Prime[n - 1]]; p(x,n)=Product[1 + f(m)*x^m, {m, 0, n}];a(n)=coefficients(p(x,n).
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MATHEMATICA
| Clear[f, P, n]; f[n_] = If[n < 2, n, Prime[n - 1]]; P[x_, n_] := P[x, n] = Product[1 + f[m]*x^m, {m, 0, n}]; Length[CoefficientList[ExpandAll[P[x, 99]], x]]; a1 = CoefficientList[ExpandAll[P[x, 99]], x]; a2 = CoefficientList[ExpandAll[P[x, 100]], x]; a = Sum[If[a1[[n]] - a2[[n]] == 0, 1, 0], {n, 1, 4951}]; Table[a2[[n]], {n, 1, 100}]
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CROSSREFS
| A147557
Sequence in context: A039658 A063675 A000943 * A197211 A032063 A037233
Adjacent sequences: A152003 A152004 A152005 * A152007 A152008 A152009
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 19 2008
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