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A316625 Terms in A259663, in ascending order. 0
1, 3, 5, 7, 11, 13, 15, 19, 21, 23, 31, 35, 47, 53, 55, 63, 79, 85, 87, 95, 99, 127, 143, 151, 191, 213, 223, 227, 255, 271, 319, 341, 351, 383, 407, 483, 511, 575, 663, 739, 767, 783, 853, 863, 895, 1023, 1175, 1251, 1279, 1365, 1407, 1535, 1599, 1807, 1887, 2047 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=1..56.

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

Cf. A259663.

Sequence in context: A047484 A036991 A165887 * A091892 A292939 A232011

Adjacent sequences:  A316622 A316623 A316624 * A316626 A316627 A316628

KEYWORD

nonn

AUTHOR

Bob Selcoe, Jul 08 2018

EXTENSIONS

More terms from Michel Marcus, Jul 10 2018

STATUS

approved

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Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)