cp's OEIS Frontend

A288313 Let b(k) denote A056240(k); the sequence lists numbers b(2*n) where for all m > n, b(2*m) > b(2*n).

%I A288313 #40 Apr 16 2024 16:35:01
%S A288313 2,4,8,15,21,33,39,51,57,69,87,93,111,123,129,141,159,177,183,201,213,
%T A288313 219,237,249,267,291,303,309,321,327,339,381,393,411,417,447,453,471,
%U A288313 489,501,519,537,543,573,579,591,597,633,669,681,687,699,717,723,753,771,789,807,813,831,843
%N A288313 Let b(k) denote A056240(k); the sequence lists numbers b(2*n) where for all m > n, b(2*m) > b(2*n).
%C A288313 This is an ascending subsequence of A056240 with even argument terms.
%C A288313 After the first three (even) terms, a(1) = b(2) = 2, a(2) = b(4) = 4, a(3) = b(6) = 8 respectively, all subsequent terms are odd (semiprime) numbers of the form 3*r, for r = primes 5, 7, 11, 13, .... The graph of all odd-valued terms a(n) for n >= 4 is a straight line (y = 3*x - 9), corresponding to b(2*n) = 3*(2*n) - 9 = 3*(2*n - 3) = 3*r, where r = 2*n - 3 is prime, and n is in sequence A098090. The sequence a(n) for n >= 4 is identical term for term to A001748(n) for n >= 3. In other words, for n >= 4, a(n) = 3*A000040(n-1).
%C A288313 If, for any even number n >= 6, n - 3 is prime, then A056240(n) belongs to this sequence.
%H A288313 Paolo Xausa, <a href="/A288313/b288313.txt">Table of n, a(n) for n = 1..10000</a>
%F A288313 a(1) = 2, a(2) = 4, a(3) = 8, and for n >= 4, a(n) = 3*A000040(n-1).
%e A288313 a(1) = 2 is included because for all n > 1, b(2n) > 2; likewise a(2) = b(4) = 4, and a(3) = b(6) = 8 are included. The first odd term, a(4) = b(8) = 15, is included since for all n > 4, b(2n) > 15. b(12) = 35 is not in this sequence because b(14) = 33 < 35, and only ascending terms are permitted.
%t A288313 Join[{2, 4, 8}, 3*Prime[Range[3, 100]]] (* _Paolo Xausa_, Apr 16 2024 *)
%Y A288313 Cf. A000040, A001748, A056240, A098090. Essentially the same as A063534.
%K A288313 nonn
%O A288313 1,1
%A A288313 _David James Sycamore_, Jun 07 2017
%E A288313 Offset changed to 1 and entry edited to reflect this change by _Michel Marcus_, Jul 03 2017