A268338 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.

1, 2, 4, 19, 23, 31, 38, 41, 46

Offset: 1

Author

David Consiglio, Jr., Feb 01 2016

Keywords

• nonn
• more

Comments

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.

Examples

			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.
49 is not a member of this sequence because it eventually reduces to 19, which cycles.
		

Crossrefs

Cf. A267703, A267970, A267969, A006666, A006370, A005186, A267970, A232711.

Programs

Python

a = 1
b = 1
prev = []
keep = []
count = 0
while b < 51:
    keep.append(a)
    flag1 = False
    flag2 = False
    if a % 2 == 0:
        a /= 2
    elif a % 4 == 1:
        a = a*3+1
    else:
        a = a*7+1
    if count > 50:
        b += 1
        a = b
        count = 0
        keep = []
    if keep.count(a) == 2 and a not in prev and a <= 50:
        prev.append(a)
        count = 0
        keep = []
        b += 1
        a = b
    count += 1
print(sorted(prev))
# David Consiglio, Jr., Feb 01 2016

Extensions

Corrected and edited by David Consiglio, Jr., Apr 20 2016