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%I #32 Apr 20 2016 14:00:18
%S 1,2,4,19,23,31,38,41,46
%N Numbers that cycle under the following transformation: if m is even, divide by 2, if m is congruent to 1 mod 4, multiply by 3 and add 1; if m is congruent to 3 mod 4, multiply by 7 and add 1.
%C Some numbers appear to grow indefinitely under these rules, but it is possible that they may eventually cycle at some point. All numbers up to 50 either cycle or transform to another number that cycles (typically 1). 51 is the first open case: it may eventually cycle or may continue to grow indefinitely.
%e 23 is a member of this sequence. 23 is congruent to 3 mod 4. As a result, 23 transforms to 23*7+1 = 162. From there 162 -> 81 -> 244 -> 122 -> 61 -> 184 -> 92 -> 46 -> 23. 23 is the least member of this cycle.
%e 49 is not a member of this sequence because it eventually reduces to 19, which cycles.
%o (Python)
%o a = 1
%o b = 1
%o prev = []
%o keep = []
%o count = 0
%o while b < 51:
%o ....keep.append(a)
%o ....flag1 = False
%o ....flag2 = False
%o ....if a % 2 == 0:
%o ........a /= 2
%o ....elif a % 4 == 1:
%o ........a = a*3+1
%o ....else:
%o ........a = a*7+1
%o ....if count > 50:
%o ........b += 1
%o ........a = b
%o ........count = 0
%o ........keep = []
%o ....if keep.count(a) == 2 and a not in prev and a <= 50:
%o ........prev.append(a)
%o ........count = 0
%o ........keep = []
%o ........b += 1
%o ........a = b
%o ....count += 1
%o print(sorted(prev))
%o # _David Consiglio, Jr._, Feb 01 2016
%Y Cf. A267703, A267970, A267969, A006666, A006370, A005186, A267970, A232711.
%K nonn,more
%O 1,2
%A _David Consiglio, Jr._, Feb 01 2016
%E Corrected and edited by _David Consiglio, Jr._, Apr 20 2016
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