A063005 -id:A063005 - cp's OEIS frontend

A056577 Difference between 3^n and highest power of 2 less than or equal to 3^n.

0, 1, 1, 11, 17, 115, 217, 139, 2465, 3299, 26281, 46075, 7153, 545747, 588665, 5960299, 9492289, 62031299, 118985033, 88519643, 1339300753, 1870418611, 14201190425, 25423702091, 7551629537

Offset: 0

Henry Bottomley, Jun 29 2000

nonn

a(n) = A227048(n,1). - Reinhard Zumkeller, Jun 30 2013

			a(3)=11 because 3^3 = 27 and 27 - 16 = 11.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Cf. A000244, A056576, A063005, A227048.

a056577 = head . a227048_row  -- Reinhard Zumkeller, Jun 30 2013

Table[# - 2^Floor@ Log2@ # &[3^n], {n, 0, 24}] (* Michael De Vlieger, Sep 30 2017 *)

a(n) = 3^n - 2^floor(log_2(3^n)) = A000244(n) - 2^A056576(n).

A063003 Difference between 3^n and the next larger or equal power of 2.

Original entry on oeis.org

0, 1, 7, 5, 47, 13, 295, 1909, 1631, 13085, 6487, 84997, 517135, 502829, 3605639, 2428309, 24062143, 5077565, 149450423, 985222181, 808182895, 6719515981, 2978678759, 43295774645, 267326277407, 252223018333, 1856180682775

Offset: 0

Jens Voß, Jul 02 2001

Harry J. Smith, Table of n, a(n) for n = 0..200

Cf. A056577, A063004, A063005.

Table[2^Ceiling@ Log2@ # - # &[3^n], {n, 0, 26}]  (* Michael De Vlieger, Sep 30 2017 *)

{ default(realprecision, 50); t=1/log(2); for (n=0, 200, write("b063003.txt", n, " ", 2^ceil(t*log(3^n)) - 3^n) ) } \\ Harry J. Smith, Aug 15 2009

a(n) = 2^(ceiling(log_2(3^n))) - 3^n.

More terms from Marc LeBrun, Jul 11 2001

A321671 Primes of the form 2^j - 3^k, for j >= 0, k >= 0.

Original entry on oeis.org

3, 5, 7, 13, 23, 29, 31, 37, 47, 61, 101, 127, 229, 269, 431, 503, 509, 997, 1021, 1319, 2039, 3853, 4093, 7949, 8111, 8191, 14197, 16141, 16381, 32687, 45853, 65293, 130343, 130829, 131063, 131071, 347141, 502829, 524261, 524287, 1028893, 1046389, 1048549

Offset: 1

Jinyuan Wang, Nov 16 2018

nonn

The numbers in A007643 are not in this sequence.
For n > 1, a(n) is of the form 8k - 1 or 8k - 3.
In this sequence, only 3 and 7 make both j and k even numbers.
Generally, the way to prove that a number is not in this sequence is to successively take residues modulo 3, 8, 5, and 16 on both sides of the equation 2^j - 3^k = x.

			7 = 2^3 - 3^0, so 7 is a term.

H. Gauchman and I. Rosenholtz (Proposers), R. Martin (Solver), Difference of prime powers, Problem 1404, Math. Mag., 65 (No. 4, 1992), 265; Solution, Math. Mag., 66 (No. 4, 1993), 269.

Cf. A000040, A007643, A192110.
Cf. A004051 (primes of the form 2^a + 3^b).
Cf. A063005.

forprime(p=1,1000,k=0;x=2;y=1;while(k

Intersection of A000040 and A192110.

More terms from Alois P. Heinz, Nov 16 2018

A063004 Difference between 2^n and the next larger or equal power of 3.

Original entry on oeis.org

0, 1, 5, 1, 11, 49, 17, 115, 473, 217, 1163, 139, 2465, 11491, 3299, 26281, 111611, 46075, 269297, 7153, 545747, 2685817, 588665, 5960299, 26269505, 9492289, 62031299, 253202761, 118985033, 625390555, 88519643, 1339300753

Offset: 0

Jens Voß, Jul 02 2001

Cf. A056577, A063003, A063005.

dp23[n_]:=Module[{t=2^n},3^Ceiling[Log[3,t]]-t]; Array[dp23,40,0] (* Harvey P. Dale, Nov 20 2015 *)

for(n=1,50,print1(3^ceil(log(2^n)/log(3))-2^n","))

a(n) = 3^ceiling(log_3(2^n)) - 2^n.

More terms from Ralf Stephan, Mar 21 2003

A328334 Forward difference of difference between 2^n and the next smaller power of 3.

Original entry on oeis.org

1, 0, 4, 2, -2, 32, 10, -34, 256, 26, 1024, 590, -278, 8192, 3262, -6598, 65536, 12974, 262144, 169994, -14306, 2097152, 1005658, -1177330, 16777216, 4856618, -18984578, 134217728, 10155130, 536870912, 298900846, -177039286, 4294967296, 1616365790, -3740837222

Offset: 0

Alois P. Heinz, Oct 12 2019

sign

a(n) is even for n >= 1.

Alois P. Heinz, Table of n, a(n) for n = 0..3323

Cf. A063005.

b:= proc(n) option remember; (t-> t-3^ilog[3](t))(2^n) end:
a:= n-> b(n+1)-b(n):
seq(a(n), n=0..40);

a(n) = A063005(n+1) - A063005(n).

cp's OEIS Frontend

A056577 Difference between 3^n and highest power of 2 less than or equal to 3^n.

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A063003 Difference between 3^n and the next larger or equal power of 2.

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A321671 Primes of the form 2^j - 3^k, for j >= 0, k >= 0.

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A063004 Difference between 2^n and the next larger or equal power of 3.

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A328334 Forward difference of difference between 2^n and the next smaller power of 3.

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