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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. 3
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 (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

Michel Marcus, Table of n, a(n) for n = 1..2000

FORMULA

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

EXAMPLE

n=1, a(1) = A056240(A298366(1)) = A056240(30) = 161;

n=24, a(24) = A056240(A298366(24)) = A056240(190) = 1969.

PROG

(PARI) A056240(n, p=n-1, m=oo)=if(n<6 || isprime(n), n, n==6, 8, until(p<3 || (n-p=precprime(p-1))*p >= m=min(m, A056240(n-p)*p), ); m);

is_A298366(n)= !isprime(n-5) && !isprime(n-3) && !(n%2) && (n>5);

lista(nn) = {for (n=0, nn, if (is_A298366(n), print1(A056240(n), ", ")); ); } \\ Michel Marcus, Apr 03 2020

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 19 12:00 EDT 2020. Contains 337880 sequences. (Running on oeis4.)