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A334149 a(n) is the number of terms required beyond the starting value n before a value larger than n first appears when following the same rules as Recamán's sequence A005132 but starting at n instead of 0.

%I A334149 #23 May 02 2020 15:56:10
%S A334149 1,2,2,4,5,5,5,7,9,10,6,8,10,12,14,8,9,11,13,15,17,9,11,13,14,16,18,
%T A334149 20,20,12,14,16,17,19,21,23,23,14,15,17,19,21,22,24,26,26,30,34,18,20,
%U A334149 22,24,26,28,29,29,33,37,37,21,23,25,27,29,31,33,33,36,19,40,44,27,26,28
%N A334149 a(n) is the number of terms required beyond the starting value n before a value larger than n first appears when following the same rules as Recamán's sequence A005132 but starting at n instead of 0.
%C A334149 For 100 <= n <= 100000 the largest number of terms to surpass the starting value n is for n = 97646 which takes 26867 terms to surpass 97646, see the link image. The longest in terms of ratio of terms required compared to starting value is for n = 133 which takes 80 terms, see the link image. The shortest ratio is for n = 82148 which only takes 8587, see the link image.
%C A334149 The first repeated number in each sequence starting from n is given in A334148.
%C A334149 The number of terms in each sequence starting from n required to reach the first repeated number is given in A334219.
%H A334149 Scott R. Shannon, <a href="/A334149/b334149.txt">Table of n, a(n) for n = 0..10000</a>
%H A334149 Scott R. Shannon, <a href="/A334149/a334149.png">Line plot of the corresponding Recamán type sequence starting with n = 97646</a>.
%H A334149 Scott R. Shannon, <a href="/A334149/a334149_1.png">Line plot of the corresponding Recamán type sequence starting with n = 133</a>.
%H A334149 Scott R. Shannon, <a href="/A334149/a334149_2.png">Line plot of the corresponding Recamán type sequence starting with n = 82148</a>.
%H A334149 Scott R. Shannon, <a href="/A334149/a334149_3.png">Plot of this sequence's terms for n = 0 to 100000</a>.
%H A334149 <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>
%e A334149 a(0) = 1 as a(0) corresponds to the standard Recamán's sequence A005132 in which the first term is 0 and it only takes one more term to reach 1 and surpass the start value.
%e A334149 a(4) = 5 as starting from 4 the sequence of visited numbers is 4,3,1,4,0,5 and it takes five more terms to reach 5 and surpass the start value 4.
%e A334149 a(12) = 10 as starting from 12 the sequence of visited numbers is 12,11,9,6,2,7,1,8,0,9,19 and it takes ten more terms to reach 19 and surpass the start value 12.
%Y A334149 Cf. A005132, A334148, A334219, A334225.
%K A334149 nonn
%O A334149 0,2
%A A334149 _Scott R. Shannon_, Apr 16 2020