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 A316625 Terms in A259663, in ascending order. 0

%I

%S 1,3,5,7,11,13,15,19,21,23,31,35,47,53,55,63,79,85,87,95,99,127,143,

%T 151,191,213,223,227,255,271,319,341,351,383,407,483,511,575,663,739,

%U 767,783,853,863,895,1023,1175,1251,1279,1365,1407,1535,1599,1807,1887,2047

%N Terms in A259663, in ascending order.

%C See A259663 for discussion of these terms in relation to Collatz sequences.

%C 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.

%C The sequence is a permutation (without repeating terms) of the following numbers:

%C 2^i-1 and 7*2^i-1 when i is odd, i >= 1;

%C 3^2^i-1 and 5^2^i-1 when i is even, i >= 2;

%C 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).

%e k=5, i=1 -- terms are least residues of 3^j*2^(12-j)-1 mod 2^(17-j), 0 <= j < 12:

%e j=0: 4096-1 mod 131072 = 4095;

%e j=1: 3*2048-1 mod 65536 = 6143;

%e j=2: 9*1024-1 mod 32768 = 9215;

%e j=3: 27*512-1 mod 16384 = 13823;

%e j=4: 81*256-1 mod 8192 = 20735 mod 8192 == 4351;

%e j=5: 243*128-1 mod 4096 = 31103 mod 4096 == 2431;

%e j=6: 729*64-1 mod 2048 = 46655 mod 2048 == 1599;

%e j=7: 2187*32-1 mod 1024 = 69983 mod 1024 == 351;

%e j=8: 6561*16-1 mod 512 = 104975 mod 512 == 15;

%e j=9: 19683*8-1 mod 256 = 157463 mod 256 == 23;

%e j=10: 59049*4-1 mod 128 = 236195 mod 128 == 35;

%e j=11: 177147*2-1 mod 64 = 354293 mod 64 == 53.

%e Note: k=5, i=0 is equivalent to starting with j=0: 15 mod 512.

%Y Cf. A259663.

%K nonn

%O 1,2

%A _Bob Selcoe_, Jul 08 2018

%E More terms from _Michel Marcus_, Jul 10 2018

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)