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A080427 a(1)=1 and, for n>1, a(n) is the smallest positive integer such that the absolute difference |a(n)-a(n-1)| has not occurred previously.

%I A080427 #8 Apr 12 2020 15:46:11
%S A080427 1,1,2,4,1,5,10,1,7,14,1,9,19,1,12,24,1,15,30,1,17,34,1,20,40,1,22,44,
%T A080427 1,25,50,1,27,54,1,29,59,1,32,64,1,35,70,1,37,74,1,39,79,1,42,84,1,45,
%U A080427 90,1,47,94,1,49,99,1,52,104,1,55,110,1,57,114,1,60,120,1,62,124,1,65,130
%N A080427 a(1)=1 and, for n>1, a(n) is the smallest positive integer such that the absolute difference |a(n)-a(n-1)| has not occurred previously.
%C A080427 It appears (1) that a(3n+2)=1 for n=1,2,3,... and (2) that the sequence {a(3n+3)-a(3n)}={3,2,2,3,3,2,3,2,3,2,2,3,3,2,2,3,3,2,...} consists only of 2's and 3's and that the sequence of the lengths of runs of consecutive 3's in {a(3n+3)-a(3n)} is given by {1,2,1,1,2,2,2,1,...}=A026465.
%H A080427 Rémy Sigrist, <a href="/A080427/b080427.txt">Table of n, a(n) for n = 1..10000</a>
%F A080427 It appears that abs(a(n+2)-a(n+1)) = A101544(n) for any n > 0. - _Rémy Sigrist_, Apr 12 2020
%o A080427 (PARI) { my(s=0, v=1, d); for (n=1, 79, print1 (v, ", "); for (w=1, oo, if (!bittest(s, d=abs(v-w)), s+=2^d; v=w; break))) } \\ _Rémy Sigrist_, Apr 12 2020
%Y A080427 Cf. A026465, A067992, A101544.
%K A080427 nonn
%O A080427 1,3
%A A080427 _John W. Layman_, Feb 19 2003