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An examination of the maximum yearly values of the conventional sunspot number <I>Rz</I> of all cycles revealed fluctuations of various intervals in the high periodicity region (exceeding 11 years), namely 2 cycles (Hale, 22 years), 3 cycles (TRC, three-cycle) and longer intervals. The 2-cycle spacings had the smallest amplitudes. According to the G-O (Gnevyshev-Ohl) rule (Gnevyshev and Ohl, 1948), the even-numbered series of the maxima of annual mean Wolf sunspot numbers <I>Rz</I> are followed by higher amplitude odd-numbered series. Kopecky (1950) generalized this relation to annual mean Wolf numbers corresponding to equivalent phases of the adjacent even-odd 11-year cycles. Therefore, we would call it the G-O-K rule. For the data of 28 cycles (cycle −4 to cycle 23), it was found that four pairs (~29%) from the fourteen even-odd pairs showed failure of the G-O-K rule. In the remaining ten pairs, the magnitudes of the odd cycles were well-correlated with the magnitudes of the preceding even cycles, but it was impossible to tell whether it would be a normal pair following the G-O-K rule or a possible case of failure. A much stronger sequence was the three-cycle sequence (TRC, low, high, higher). The 2-cycle oscillations were embedded into the TRC until the G-O-K rule failures occurred as in cycle 23. The patterns of cycle 17 (low), 18 (high), 19 (higher); 20 (low), 21 (high), 22 (higher) were noticed and used by Ahluwalia (1995, 1998) to predict a low value for cycle 23, which was accurate. However, in the earlier data, the preceding sequence (14, 15, 16) was rather uncertain, and before that for seven cycles (cycles 8-14), there were no TRC sequences at all. During the twelve cycles −4 to 7, there were only three isolated TRC sequences (one doubtful). <br><br> In view of this chequered history of TRC, it is doubtful whether the present TRC pattern (cycles 17–23) would persist in the near future. Spectral analysis showed that in the first half (cycles −4 to 9), larger periodicities (reminiscent of the Gleissberg cycle of ~80 years) prevailed. but in the latter half, periodicities were different (3-year cycle was predominant) and the matching was not good. In particular, the points for the recent cycles 21, 22 seemed to deviate considerably from the constructed series, thus introducing unreliability in predictions for the future by using extrapolation of periodicities.