cp's OEIS Frontend

A268034 A268032 with repeated 1's removed.

%I A268034 #13 Aug 15 2025 05:55:11
%S A268034 3,5,11,3,21,3,5,43,3,5,11,3,85,3,5,11,3,21,3,5,171,3,5,11,3,21,3,5,
%T A268034 43,3,5,11,3,341,3,5,11,3,21,3,5,43,3,5,11,3,85,3,5,11,3,21,3,5,683,3,
%U A268034 5,11,3,21,3,5,43,3,5
%N A268034 A268032 with repeated 1's removed.
%C A268034 Records appear to be given by A001045 Jacobsthal numbers.
%C A268034 (a(n)-1)/2 appears to be A085358.
%C A268034 The terms between the A001045(n+3) are:
%C A268034 3
%C A268034 5
%C A268034 11
%C A268034       3,
%C A268034 21
%C A268034       3, 5,
%C A268034 43
%C A268034       3, 5, 11, 3,
%C A268034 85
%C A268034       3, 5, 11, 3, 21, 3, 5,
%C A268034 171
%C A268034       3, 5, 11, 3, 21, 3, 5, 43, 3, 5, 11, 3,
%C A268034 341
%C A268034       3, 5, 11, 3, 21, 3, 5, 43, 3, 5, 11, 3, 85, 3, 5, 11, 3, 21, 3, 5,
%C A268034 683
%C A268034 This gives the same sequence. Every column has the same number.
%C A268034 By rows, there are 0, 0, 1, 2, 4, 7, 12, 20, ... apparently = Fibonacci(n+1) - 1 = A000071 terms.
%C A268034 From _Paul Curtz_, Jan 26 2016: (Start)
%C A268034 a(n) is also in
%C A268034   0,  1,  1  0,  3, 0,  1,  5, 0, ...  equivalent to A035614(n)
%C A268034   1,  1,  3, 1,  5, 1,  1, 11, 1, ...  equivalent to A035612(n)
%C A268034   1,  3,  5, 1, 11, 1,  3, 21, 1, ... (compare to A268032)
%C A268034   3,  5, 11, 3, 21, 3,  5, 43, 3, ...  a(n) (equivalent to a3(n) in A035612)
%C A268034   5, 11, 21, 5, 43, 5, 11, 85, 5, ...
%C A268034 etc.
%C A268034 Every vertical comes from A001045 (*).
%C A268034 Second row: first one removing all 0's.
%C A268034 Third row: second one removing a part of 1's respecting (*)
%C A268034 Fourth row: third one removing all 1's.
%C A268034 etc.
%C A268034 The offset 0 is homogeneous to these sequences. (End)
%e A268034 A268032 begins 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 3, 1, 1, 1, 21, ... hence this sequence begins 3, 5, 11, 3, 21, ...
%Y A268034 Cf. A000071, A001045, A035612, A035614, A085358, A268032.
%K A268034 nonn
%O A268034 1,1
%A A268034 _Jeremy Gardiner_, Jan 24 2016