cp's OEIS Frontend

A226056 a(n) = Number of common trailing terms on the row n of tables A225632 and A225642.

%I A226056 #16 Feb 11 2025 16:37:06
%S A226056 1,1,1,2,2,2,3,2,2,3,3,3,3,5,1,1,2,4,1,5,2,2,4,5,2,2,1,2,4,6,1,5,2,4,
%T A226056 1,4,3,5,1,4,1,7,6,8,4,4,4,9,3,2,1,5,4,9,2,2,2,3,2,8,6,9,1,1,1,2,4,8,
%U A226056 3,1,4,7,8,8,2,3,3,3,1,8,1,2,3,10,10
%N A226056 a(n) = Number of common trailing terms on the row n of tables A225632 and A225642.
%C A226056 The positions n, in which a(n)=1: 0, 1, 2, 14, 15, 18, 26, 30, 34, 38, 40, 50, 62, 63, 64, 69, 78, 80, ...
%C A226056 By convention, a(0)=1 as this applies also to the tables A225630 and A225640, whose columns start from zero.
%C A226056 In other words, a(n) = 1 + distance from the first common term on column n (A226055(n)) of tables A225630 and A225640 to the respective fixed point, A003418(n).
%F A226056 a(n) = A225634(n)-A225638(n) = A225644(n)-A225639(n).
%e A226056 Row 7 of A225632 is: 1, 12, 84, 420;
%e A226056 Row 7 of A225642 is: 7, 84, 420;
%e A226056 the last two terms (84 and 420) are common to them, thus a(7)=2.
%e A226056 Row 14 of A225632 is: 1, 84, 1260, 16380, 180180, 360360;
%e A226056 Row 14 of A225642 is: 14, 630, 8190, 90090, 360360;
%e A226056 they have no common term until as the last term of those rows (which is A003418(14)=360360), thus a(14)=1.
%o A226056 (Scheme)
%o A226056 (define (A226056 n) (- (A225634 n) (A225638 n)))
%o A226056 (define (A226056 n) (- (A225644 n) (A225639 n))) ;; Alternative definition.
%Y A226056 Cf. A226055, A225634, A225644, A225638, A225639.
%K A226056 nonn
%O A226056 0,4
%A A226056 _Antti Karttunen_, May 24 2013