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.

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

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: A025342 A189639 A348426 * A250644 A060641 A209282

Adjacent sequences: A298612 A298613 A298614 * A298616 A298617 A298618

Keyword

nonn

Author

David James Sycamore, Jan 26 2018

Status

approved