A114216 -id:A114216 - cp's OEIS frontend

A114217 Numbers n such that A114216(n)=1.

Original entry on oeis.org

1, 2, 5, 12, 14, 20, 75, 33900, 78493252

Offset: 1

Zak Seidov, Nov 18 2005

nonn

Is 33900 the last term? No other terms <10000000. Cf. A114218 values of k when A114216(n)=1.

a(10) > 4*10^9. [From Donovan Johnson, May 13 2010]

Cf. A114216, A114218.

a(9) from Donovan Johnson, May 13 2010

A114218 Values of k when A114216(n)=1.

Original entry on oeis.org

1, 2, 4, 6, 6, 7, 9, 19, 31

Offset: 1

Zak Seidov, Nov 18 2005

nonn

The last term 19 corresponds to n=33900 in A114216: A114216(33899) = 123729 and 33900th prime is 400559, hence 123729 + 400559 = 524288 = 2^19 and A114216(33900) = 1. Cf. A114217 values of n such that A114216(n) = 1.

Cf. A114216, A114217.

a(9) from Donovan Johnson, May 13 2010

A114221 Numbers m such that A114216(m)=3.

Original entry on oeis.org

3, 7, 15, 24, 45, 76, 161, 309, 456, 55621039

Offset: 1

Zak Seidov, Nov 18 2005

a(11) (if it exists) > 37607912018. - Hiroaki Yamanouchi, Sep 24 2014

Cf. A114216, A114218.

Numbers m such that A114216(m)=k: A114217 (k=1), A114222 (k=7), A114223 (k=11), A114224 (k=17).

a(10) from Hiroaki Yamanouchi, Sep 24 2014

A114222 Numbers m such that A114216(m) = 7.

Original entry on oeis.org

6, 16, 23, 80, 9610965

Offset: 1

Zak Seidov, Nov 18 2005

a(6) (if it exists) > 37607912018. - Hiroaki Yamanouchi, Sep 24 2014

Cf. A114216, A114218.

Numbers m such that A114216(m)=k: A114217 (k=1), A114221 (k=3), A114223 (k=11), A114224 (k=17).

a(5) from Hiroaki Yamanouchi, Sep 24 2014

A114223 Numbers m such that A114216(m) = 11.

Original entry on oeis.org

8, 158, 959, 1523, 2155

Offset: 1

Zak Seidov, Nov 18 2005

a(6) (if it exists) > 37607912018. - Hiroaki Yamanouchi, Sep 24 2014

Cf. A114216, A114218.

Numbers m such that A114216(m)=k: A114217 (k=1), A114221 (k=3), A114222 (k=7), A114224 (k=17).

A114224 Numbers m such that A114216(m) = 17.

Original entry on oeis.org

9, 1897, 62815, 192282, 21138551

Offset: 1

Zak Seidov, Nov 18 2005

a(6) (if it exists) > 37607912018. - Hiroaki Yamanouchi, Sep 24 2014

Numbers m such that A114216(m)=k: A114217 (k=1), A114221 (k=3), A114222 (k=7), A114223 (k=11).

a(4)-a(5) from Hiroaki Yamanouchi, Sep 24 2014

A208884 a(n) = (a(n-1) + n)/2^k where 2^k is the largest power of 2 dividing a(n-1) + n, for n>1 with a(1)=1.

Original entry on oeis.org

1, 3, 3, 7, 3, 9, 1, 9, 9, 19, 15, 27, 5, 19, 17, 33, 25, 43, 31, 51, 9, 31, 27, 51, 19, 45, 9, 37, 33, 63, 47, 79, 7, 41, 19, 55, 23, 61, 25, 65, 53, 95, 69, 113, 79, 125, 43, 91, 35, 85, 17, 69, 61, 115, 85, 141, 99, 157, 27, 87, 37, 99, 81, 145, 105, 171

Offset: 1

Paul D. Hanna, Mar 02 2012

nonn

In other words, to get a(n), add n to a(n-1) and compute the odd part (A000265) of the sum. - Ralf Stephan, Oct 27 2013
POSITIONS of odd numbers in the initial 7000000 terms begin:
1: [1, 7, 69, 285, 3601, 5167, 92989, 112651, 6933175, ...];
3: [2, 3, 5, 613, 8461, 46749, 81237, 102171, 126661, 3309589, ...];
5: [13, 97, 2431, 92095, ...];
7: [4, 33, 3167, 78095, 2723179, ...];
9: [6, 8, 9, 21, 27, 303, 2017, 3239, 3765, 6753, 28387, 251451, ...];
11: [75, 15823, 28221, 4091959, 5820487, ...];
13: [22975, 42391, 3729249, ...];
15: [11, 22587, 2527579, 6954893, ...];
17: [15, 51, 3121, 13433, 74763, 376853, 576439, 896899, ...];
19: [10, 14, 25, 35, 291, 77747, 757319, 1227595, 2307099, ...];
21: [1417, 1557, 712229, 2563807, ...];
23: [37, 127, 609, 2211, 5563, 199901, ...];
25: [17, 39, 221, 1145, 3425, 17593, 4318897, ...];
27: [12, 23, 59, 73, 289, 1149, 3393, 20439, 37107, ...];
29: [573, 33315, 61505, 467047, 491359, 1170709, 1492309, 2498593, 3017011, ...];
31: [19, 22, 229, 409, 6199, 60529, 3602675, 4108215, 4604929, ...]; ...
From Ya-Ping Lu, Jun 25 2020: (Start)
Conjecture: For any given odd number m, there exists a number n_max such that all odd numbers <= m can be found in the sequence a(n) with n <= n_max. For example:
m = 1, n_max = 1;
m = 3, n_max = 2;
m = 5, n_max = 13;
m = 11, n_max = 75
m = 13, n_max = 22975;
m = 305, n_max = 1025715;
m = 749, n_max = 14695985;
m = 795, n_max = 150788015;
m = 7525, n_max = 31129547917;
...
If the conjecture above is true, this sequence contains all odd numbers. (End)

			a(2) = 1 + 2 = 3;
a(3) = (3 + 3)/2 = 3;
a(4) = 3 + 4 = 7;
a(5) = (7 + 5)/4 = 3;
a(6) = 3 + 6 = 9;
a(7) = (9 + 7)/16 = 1; ...

Paul D. Hanna, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of the parity of n)

Cf. A069834, A090895, A114216, A335817.

a[1]=1; a[n_] := a[n] = #/2^IntegerExponent[#, 2] &@ (n + a[n-1]); Array[a, 70] (* Giovanni Resta, Jun 25 2020 *)

{a(n)=if(n==1, 1, (a(n-1)+n)/2^valuation(a(n-1)+n,2))}

{A=vector(1024); a(n)=A[n]=if(n==1, 1, (A[n-1]+n)/2^valuation(A[n-1]+n,2))}
for(n=1,#A,print1(a(n),", "))

cp's OEIS Frontend

A114217 Numbers n such that A114216(n)=1.

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A114218 Values of k when A114216(n)=1.

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A114221 Numbers m such that A114216(m)=3.

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A114222 Numbers m such that A114216(m) = 7.

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A114223 Numbers m such that A114216(m) = 11.

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A114224 Numbers m such that A114216(m) = 17.

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A208884 a(n) = (a(n-1) + n)/2^k where 2^k is the largest power of 2 dividing a(n-1) + n, for n>1 with a(1)=1.

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