cp's OEIS Frontend

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.

%I A298615 #28 Apr 20 2020 03:50:06
%S A298615 161,217,329,371,427,511,581,623,1246,791,1417,1243,1469,2071,917,973,
%T A298615 1507,1529,1057,1099,1169,1211,1267,1969,1991,1393,2167,2189,2587,
%U A298615 1477,2954,2321,2743,1631,1687,2629,2651,1757,1799,1841,1897,1981,3091,3113,2051,4102
%N 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.
%C A298615 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).
%H A298615 Michel Marcus, <a href="/A298615/b298615.txt">Table of n, a(n) for n = 1..2000</a>
%F A298615 a(n) = A056240(A298366(n)).
%e A298615 n=1, a(1) = A056240(A298366(1)) = A056240(30) = 161;
%e A298615 n=24, a(24) = A056240(A298366(24)) = A056240(190) = 1969.
%o A298615 (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);
%o A298615 is_A298366(n)= !isprime(n-5) && !isprime(n-3) && !(n%2) && (n>5);
%o A298615 lista(nn) = {for (n=0, nn, if (is_A298366(n), print1(A056240(n), ", ")););} \\ _Michel Marcus_, Apr 03 2020
%Y A298615 Cf. A056240, A288313, A297150, A298252, A298366, A005843.
%K A298615 nonn
%O A298615 1,1
%A A298615 _David James Sycamore_, Jan 26 2018