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A298615 Let b(k) be A056240(k); this sequence lists numbers b(2n) such that there is at least one m>n for which b(2m)<b(2n) belongs to A297150 2
161, 217, 329, 371, 427, 511, 581, 623, 1246, 791, 1417, 1243, 1469, 2071, 917, 973, 1507, 1529, 1057, 1099, 1169, 1211, 1267, 1969, 1991, 1393, 2167, 2189, 2587, 1477, 2954, 2321, 2743, 1631, 1687, 2629, 2651, 1757, 1799, 1841, 1897, 1981, 3091, 3113, 2051, 4102, 3223, 3809, 7618, 2219, 4069, 3487, 4121, 5947, 2317, 2359, 4718, 3707, 2471, 2513, 5026, 2569, 2611, 2681, 2723, 5446, 2807, 5161, 2863, 5726, 4499, 2947, 4609, 4631, 3031, 3101, 3143, 6286, 3269, 6019, 5137, 6071, 3353, 6706, 3437, 6331, 3521, 3563, 7126, 5599, 6617, 3661, 5731, 5753, 6799, 8857, 8891, 9937, 3787, 3829, 7658, 6017, 3899, 3941, 3997, 4039, 8078, 6347, 4109, 4151, 4207, 4249, 4333 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For even number n, if n-5 and n-3 are both composite then A056240(n) belongs to this sequence. The union of terms in this sequence together with those in A288313 and A297150 combine to make A056240(2n), for n>=3. A288313(n)=A056240(A298252(n)), A297150(n)=A056240(A297925(n)), and the terms of this sequence correspond to A056240(A298366). Distinct sequences A298252, A297925, and A298366 form a partition of the nonnegative even integers (A005843)>=6. These partitions holds because any even integer n>=6 is such that, either n-3 is prime (A298252), or n-5 is prime but n-3 is composite (A297925), or both n-5 and n-3 are composite (A298366).

LINKS

Table of n, a(n) for n=1..113.

FORMULA

a(n) = A056240(A298366(n)).

EXAMPLE

n=1, a(n)=A056240(A298366(1))=A056240(30)=161; n=24, a(24)=A056240(A298366(24))=A056240(190)=1969.

CROSSREFS

Cf. A056240, A288313, A297150, A298252, A298366, A005843.

Sequence in context: A025350 A025342 A189639 * A250644 A060641 A209282

Adjacent sequences:  A298612 A298613 A298614 * A298616 A298617 A298618

KEYWORD

nonn

AUTHOR

David James Sycamore, Jan 26 2018

STATUS

approved

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Last modified October 15 05:43 EDT 2019. Contains 328026 sequences. (Running on oeis4.)