OFFSET
1,2
COMMENTS
See A259663 for discussion of these terms in relation to Collatz sequences.
There are k terms in the interval [2^k, 2^(k+1)], k >= 1; terms in each interval are of the form 2^k + a(n) for some n.
The sequence is a permutation (without repeating terms) of the following numbers:
2^i-1 and 7*2^i-1 when i is odd, i >= 1;
3^2^i-1 and 5^2^i-1 when i is even, i >= 2;
For fixed k >= 4: least residues of 3^j*(2^(2^(k-3) + i*2^(k-2) - j)) - 1 mod 2^(2^(k-3) + i*2^(k-2) + k-j), i >= 0, 0 <= j < 2^(k-3) + i*2^(k-2) . (See example).
EXAMPLE
k=5, i=1 -- terms are least residues of 3^j*2^(12-j)-1 mod 2^(17-j), 0 <= j < 12:
j=0: 4096-1 mod 131072 = 4095;
j=1: 3*2048-1 mod 65536 = 6143;
j=2: 9*1024-1 mod 32768 = 9215;
j=3: 27*512-1 mod 16384 = 13823;
j=4: 81*256-1 mod 8192 = 20735 mod 8192 == 4351;
j=5: 243*128-1 mod 4096 = 31103 mod 4096 == 2431;
j=6: 729*64-1 mod 2048 = 46655 mod 2048 == 1599;
j=7: 2187*32-1 mod 1024 = 69983 mod 1024 == 351;
j=8: 6561*16-1 mod 512 = 104975 mod 512 == 15;
j=9: 19683*8-1 mod 256 = 157463 mod 256 == 23;
j=10: 59049*4-1 mod 128 = 236195 mod 128 == 35;
j=11: 177147*2-1 mod 64 = 354293 mod 64 == 53.
Note: k=5, i=0 is equivalent to starting with j=0: 15 mod 512.
CROSSREFS
KEYWORD
nonn
AUTHOR
Bob Selcoe, Jul 08 2018
EXTENSIONS
More terms from Michel Marcus, Jul 10 2018
STATUS
approved