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 A330261 Start with an empty stack S; for n = 1, 2, 3, ..., interpret the binary representation of n from left to right as follows: in case of bit 1, push the number 1 on top of S, in case of bit 0, replace the two numbers on top of S, say u on top of v, with u-v; a(n) gives the number on top of S after processing n. 3
 1, 0, 1, -1, 1, 0, 1, -2, 1, 1, 1, -1, 1, 0, 1, -3, 1, 4, 1, 0, 1, 0, 1, -2, 1, 1, 1, -1, 1, 0, 1, -4, 1, 5, 1, 7, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -3, 1, 2, 1, 0, 1, 0, 1, -2, 1, 1, 1, -1, 1, 0, 1, -5, 1, 5, 1, -4, 1, 0, 1, 3, 1, -3, 1, 1, 1, 0, 1, -2, 1, -2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS This sequence is a variant of A308551. After processing n, S has A268289(n) elements. Every integer appears infinitely many times in the sequence: - the effect of the binary string b(0) = "110" is to leave 0 on top of S, - the effect of the binary string b(1) = "1" is to leave 1 on top of S, - the effect of the binary string b(-1) = "11100" is to leave -1 on top of S, - let "|" denote the binary concatenation, - for any k > 0:    - the effect of b(k+1) = b(-1)|b(k)|"0" is to leave k+1 on top of S,    - the effect of b(-k-1) = b(1)|b(-k)|"0" is to leave -k-1 on top of S, - for any k, for any n > 0, if the binary representation of n ends with b(k), then a(n) = k, QED, - see A330264 for the values in order of appearance. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..8192 Rémy Sigrist, Scatterplot of the first 2^20 terms Rémy Sigrist, PARI program for A330261 FORMULA a(2*k-1) = 1 for any k > 0. EXAMPLE The first terms, alongside the binary representation of n and the evolution of stack S, are:   n   a(n)  bin(n)  S   --  ----  ------  ------------------------------------------------------------    1     1       1  () -> (1)    2     0      10  (1) -> (1,1) -> (0)    3     1      11  (0) -> (0,1) -> (0,1,1)    4    -1     100  (0,1,1) -> (0,1,1,1) -> (0,1,0) -> (0,-1)    5     1     101  (0,-1) -> (0,-1,1) -> (0,2) -> (0,2,1)    6     0     110  (0,2,1) -> (0,2,1,1) -> (0,2,1,1,1) -> (0,2,1,0)    7     1     111  (0,2,1,0) -> (0,2,1,0,1) -> (0,2,1,0,1,1) -> (0,2,1,0,1,1,1) PROG (PARI) See Links section. CROSSREFS Cf. A268289, A308551, A330261, A330264. Sequence in context: A206706 A302354 A000164 * A157746 A349082 A281010 Adjacent sequences:  A330258 A330259 A330260 * A330262 A330263 A330264 KEYWORD sign,base AUTHOR Rémy Sigrist, Dec 07 2019 STATUS approved

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Last modified January 26 12:39 EST 2022. Contains 350598 sequences. (Running on oeis4.)