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

Author

David James Sycamore, Jan 26 2018

Keywords

• nonn

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).

Examples

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

Links

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

Crossrefs

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

Programs

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

Formula

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