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A190895
Auxiliary r(n) sequence used to prove some properties about Rowland's sequence: r(1) = 1, and r(n) = 1/2*(c(n)+1), where c(n) is A190894, for n>1.
1
1, 5, 6, 11, 12, 23, 24, 47, 48, 50, 51, 101, 102, 105, 110, 111, 117, 233, 234, 467, 468, 470, 471, 941, 942, 945, 1889, 1890, 3779, 3780, 7559, 7560, 7566, 15131, 15132, 15158, 15159, 15162, 30323, 30324, 60647, 60648, 60650, 60651, 60701, 60702, 121403, 121404, 242807, 242808, 242810
OFFSET
1,2
COMMENTS
This sequence is matched with another auxiliary sequence called c(n) (A190894). Rowland's sequence (A106108) can be easily described in terms of c(n) and r(n). Also, they can be used to prove easily that the difference between two consecutive terms is always 1 or a prime.
This sequence is related to Rowland's sequence (A106108) with initial condition a(1)=7.
Sequence r(n) satisfies 2r(n) - 1 = c(n), for any n>1.
For further information, see the references.
LINKS
F. Chamizo, D. Raboso, and S. Ruiz-Cabello, On Rowland's sequence, Electronic J. Combin., Vol. 18(2), 2011, #P10.
E. S. Rowland, A natural prime-generating recurrence, J. Integer Seq., 11(2): Article 08.2.8, 13, 2008.
EXAMPLE
For n = 2, r(2) = 1/2 * (c(2) + 1) = 1/2 * (9 + 1) = 5.
For n = 3, r(3) = 1/2 * (c(3) + 1) = 1/2 * (11 + 1) = 6.
CROSSREFS
Sequence in context: A369273 A277095 A332482 * A129286 A334813 A083450
KEYWORD
nonn
AUTHOR
STATUS
approved