A367578 - OEIS

%I #27 Nov 30 2023 01:25:51

%S 0,1,2,14,35,78,21,103,92,53,28,60,146,145,84,26,68,134,215,173,122,

%T 91,62,46,22,84,56,11,72,55,30,83,75,38,91,180,169,168,77,164,93,44,

%U 10,51,56,41,105,94,153,112,81,109,98,197,116,45,109,58,153,234,202,160,139,138,47,131,202,190

%N a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-1) - CT(a(n-2),a(n-1)) if nonnegative and not already in the sequence, else a(n) = a(n-1) + CT(a(n-2),a(n-1)), where CT(a,b) is the Comma transform (cf. A367360) of a and b.

%C This is a variation of Recamán's sequence A005132, where the step size is calculated from the Comma transform of the previous two terms, see A367360 and A121805. As the maximum step size is 99, it is likely that many numbers never appear. In the first 10 million terms the smallest numbers that do appear are 0,1,2,8,10,11,14,17,21,22. The first number to appear twice is 84. The terms show a broadly repetitive pattern that repeats every order of magnitude, although slight differences are still present; see the two attached images.

%H Scott R. Shannon, <a href="/A367578/b367578.txt">Table of n, a(n) for n = 0..10000</a>.

%H Scott R. Shannon, <a href="/A367578/a367578.png">Image of the first 100000 terms</a>. The green line is a(n) = n.

%H Scott R. Shannon, <a href="/A367578/a367578_1.png">Image of the first 10000000 terms</a>.

%e a(2) = 2 as CT(a(0),a(1)) = CT(0,1) = 1, so a(2) = a(1) + 1 = 2.

%e a(3) = 14 as CT(a(1),a(2)) = CT(1,2) = 12, so a(3) = a(2) + 12 = 14.

%e a(7) = 21 as CT(a(5),a(6)) = CT(35,78) = 57, so a(7) = a(6) - 57 = 21, as 21 is nonnegative and not already in the sequence.

%Y Cf. A367360, A005132, A121805.

%K nonn,base,look

%O 0,3

%A _Scott R. Shannon_, Nov 25 2023