A244076 -id:A244076 - cp's OEIS frontend

A244071 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 19, 37, 73}.

777149, 790841, 1106681, 1715053, 3079469, 3580901, 4485343, 4570619, 4953397, 6055001, 8482363, 9203917, 9375479, 12000697, 12973451, 15728953, 17710319, 17789279, 19026359, 20512783, 21444847, 25245791, 25955141, 26829581, 28482703, 28492573, 28833011, 28949519

Offset: 1

Pierre CAMI, Jun 19 2014

nonn

For n > 144 a(n) = a(n-144) + 140100870, the first 144 values are in the table.

Pierre CAMI, Table of n, a(n) for n = 1..144

Cf. A076337, A244071, A244072, A244073, A244074, A244076.

For n > 144, a(n) = a(n-144) + 140100870.

A244070 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 17, 241}.

Original entry on oeis.org

509203, 762701, 992077, 1247173, 1254341, 1330207, 1330319, 1730653, 1730681, 1976473, 2313487, 2344211, 2554843, 3177553, 3292241, 3419789, 3423373, 3661529, 3661543, 3784439, 4384979, 4442323, 4506097, 4507889, 4626967, 5049251, 5050147, 6610811, 7117807, 7576559, 7629217, 8086751, 8101087, 8252819, 8253043, 8643209, 9053711, 9053767, 9545351, 9560713, 9666029, 10219379, 10280827, 10581097, 10609769, 10702091, 10913233, 10913681

Offset: 1

Pierre CAMI, Jun 19 2014

nonn

For n > 48, a(n) = a(n-48) + 11184810, the first 48 values are given in the data.

Cf. A076337, A244071, A244072, A244073, A244074, A244076.

For n > 48, a(n) = a(n-48) + 11184810.

A244072 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 19, 37, 109}.

Original entry on oeis.org

2136283, 2251349, 2924861, 3781541, 8010517, 10645867, 11124703, 16413457, 16593431, 17713229, 21992527, 22146359, 23572417, 23835883, 23909173, 24359437, 24688477, 25124999, 26711801, 26880179, 27094349, 28151593, 30577271, 32126257

Offset: 1

Pierre CAMI, Jun 19 2014

nonn

For n > 144 a(n) = a(n-144) + 209191710, the first 144 values are in the table.

Pierre CAMI, Table of n, a(n) for n = 1..144

Cf. A076337, A244070, A244071, A244073, A244074, A244076.

For n > 144, a(n) = a(n-144) + 209191710.

A244073 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 19, 73, 109}.

Original entry on oeis.org

1744117, 6975809, 7790113, 11942443, 13006807, 16861093, 16882181, 17207051, 20003369, 20147891, 21013423, 25638127, 42918821, 45113083, 47285977, 48635609, 49884041, 53335151, 53538727, 56592041, 63412693, 63750101, 64062209, 65739209

Offset: 1

Pierre CAMI, Jun 19 2014

nonn

For n > 144 a(n) = a(n-144) + 412729590, the first 144 values are in the table.

Pierre CAMI, Table of n, a(n) for n = 1..144

Cf. A076337, A244070, A244071, A244072, A244074, A244076.

For n > 144, a(n) = a(n-144) + 412729590.

A244074 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 37, 73, 109}.

Original entry on oeis.org

1830187, 4643293, 17041931, 20787701, 50462309, 52363777, 66659587, 68026001, 71604733, 71817943, 88558303, 91609361, 93193151, 97363751, 118421557, 122606647, 123765359, 124808009, 131118733, 131408411, 134320001, 135411719, 139778591, 142339723

Offset: 1

Pierre CAMI, Jun 19 2014

nonn

For n > 144, a(n) = a(n-144) + 803736570, the first 144 values are in the table.

Pierre CAMI, Table of n, a(n) for n = 1..144

Cf. A076337, A244070, A244071, A244072, A244073, A244076.

For n > 144, a(n) = a(n-144) + 803736570.

A244561 Odd integers m such that for every integer k > 0, m*2^k+1 has a divisor in the set {3, 5, 7, 13, 17, 241}.

Original entry on oeis.org

271129, 271577, 482719, 575041, 603713, 903983, 965431, 1518781, 1624097, 1639459, 2131043, 2131099, 2541601, 2931767, 2931991, 3083723, 3098059, 3555593, 3608251, 4067003, 4573999, 6134663, 6135559, 6557843, 6676921, 6678713, 6742487, 6799831, 7400371, 7523267, 7523281, 7761437, 7765021, 7892569, 8007257, 8629967, 8840599, 8871323, 9208337, 9454129, 9454157, 9854491, 9854603, 9930469, 9937637, 10192733, 10422109, 10675607

Offset: 1

Pierre CAMI, Jun 30 2014

nonn

For n > 48, a(n) = a(n-48) + 11184810; the first 48 values are in the data.
The set {3, 5, 7, 13, 17, 241} is the set of prime divisors of 2^24 - 1. Hence for every p in the set the multiplicative order of 2 modulo p divides 24. Note that twice the product of {3, 5, 7, 13, 17, 241} is 11184810. - Jeppe Stig Nielsen, Mar 10 2019
Subset of provable Sierpiński numbers A076336. - Jeppe Stig Nielsen, Mar 10 2019

Cf. A076336, A244070, A244071, A244072, A244073, A244074, A244076.

D=[3, 5, 7, 13, 17, 241];P=2*lcm(D);M=lcm(apply(d->znorder(Mod(2,d)),D));forstep(k=1,+oo,2,if(k%P==1,print();print());for(n=0,M-1,for(i=1,#D,k*Mod(2,D[i])^n+1==0 && next(2));next(2));print1(k,", ")) \\ Jeppe Stig Nielsen, Mar 10 2019

For n > 48, a(n) = a(n-48) + 11184810.

A243974 Integers n not of form 3m+1 such that for any integer k>0, n*10^k-1 has a divisor in the set { 7, 11, 13, 37 }.

Original entry on oeis.org

10176, 17601, 19361, 25827, 27147, 27686, 35916, 36048, 45462, 47213, 48036, 49248, 54638, 62864, 64184, 64899, 72953, 73085, 82499, 85073, 86285, 93435, 101760, 101936

Offset: 1

Pierre CAMI, Jun 16 2014

nonn

For n>24 a(n) = a(n-24) + 111111, the first 24 values are in the data.

If n is of form 3m+1 then n*10^k-1 is always divisible by 3. - Jens Kruse Andersen, Jul 09 2014

			10176*10^k-1 is divisible by 11 for k of form 6m, 6m+2, 6m+4, by 7 for k of form 6m+1, by 37 for 6m+3 (and also 6m), and by 13 for 6m+5. This covers all k. {7, 11, 13, 37} is called a covering set. - _Jens Kruse Andersen_, Jul 09 2014

Cf. A076337, A243969, A243974, A244070, A244071, A244072, A244073, A244074, A244076.

For n > 24, a(n) = a(n-24) + 111111.

Definition corrected by Jens Kruse Andersen, Jul 09 2014

A244211 Integers n such that for every integer k>0, n*6^k-1 has a divisor in the set { 7, 13, 31, 37, 43 }.

Original entry on oeis.org

133946, 213410, 299144, 33845, 367256, 803676, 1214450, 1250446, 1280460, 1704478, 1780150, 1792762, 1794864, 2003070, 2004962, 2203536, 2798489, 3014465, 3027709, 3041998, 3053350, 3194549, 3326301, 4244794

Offset: 1

Pierre CAMI, Jun 23 2014

nonn

For n > 24 a(n) = a(n-24) + 4488211, the first 24 values are in the data.

When the number a(n) has 1 or 6 as the last digit, the number a(n)*6^k-1 is always divisible by 5 and always has another divisor in the set { 7, 13, 31, 37, 97 } for every k.

Cf. A076337, A243969, A244070, A244071, A244072, A244073, A244074, A244076.

For n > 24, a(n) = a(n-24) + 4488211.

A244545 Integers n such that for every integer k>0, n*6^k+1 has a divisor in the set { 7, 13, 31, 37, 43 }.

Original entry on oeis.org

243417, 1161910, 1293662, 1434861, 1446213, 1460502, 1473746, 1689722, 2284675, 2483249, 2485141, 2693347, 2695449, 2708061, 2783733, 3207751, 3237765, 3273761, 3684535, 4120955, 4154366, 4189067, 4274801, 4354265

Offset: 1

Pierre CAMI, Jun 29 2014

nonn

For n > 24, a(n) = a(n-24) + 4488211, the first 24 values are in the data.

When the number a(n) has 4 or 9 as the last digit, the number a(n)*6^k-1 is always divisible by 5 and always has a divisor in the set { 7, 13, 31, 37, 97 } for every k.

Cf. A076337, A243969, A244070, A244071, A244072, A244073, A244074, A244076, A244211.

For n > 24 a(n) = a(n-24) + 4488211.

A244566 Odd integers n such that for every integer k>0, n*2^k+1 has a divisor in the set { 3, 5, 7, 13, 17, 97, 257 }.

Original entry on oeis.org

327739, 5455789, 8879993, 9043831, 21823667, 25763447, 29949559, 75037639, 92732027, 119863547, 119879899, 122091961, 146880319, 151060223, 152106751, 163378771, 181339441, 182384417, 182646049, 218039041, 232190537

Offset: 1

Pierre CAMI, Jun 30 2014

These are the Sierpiński numbers (A076336) with covering set {3, 5, 7, 13, 17, 97, 257}. - David W. Wilson, Jul 18 2014

For n > 96, a(n) = a(n-96) + 1156954890, the first 96 values are in the table.

Pierre CAMI, Table of n, a(n) for n = 1..96

Cf. A076336, A244076, A244561, A244562, A244563, A244564, A244565.

is(n)=my(G=578477445,t=Mod(n,G)); for(k=1,768,t*=2; if(gcd(t+1, G)==1, return(0))); n%2 \\ Charles R Greathouse IV, Jul 18 2014

For n > 96, a(n) = a(n-96) + 1156954890.

cp's OEIS Frontend

A244071 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 19, 37, 73}.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A244070 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 17, 241}.

Views

Author

Keywords

Comments

Crossrefs

Formula

A244072 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 19, 37, 109}.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A244073 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 19, 73, 109}.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A244074 Odd integers n such that for every integer k>0, n*2^k-1 has a divisor in the set {3, 5, 7, 13, 37, 73, 109}.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A244561 Odd integers m such that for every integer k > 0, m*2^k+1 has a divisor in the set {3, 5, 7, 13, 17, 241}.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

Formula

A243974 Integers n not of form 3m+1 such that for any integer k>0, n*10^k-1 has a divisor in the set { 7, 11, 13, 37 }.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

Extensions

A244211 Integers n such that for every integer k>0, n*6^k-1 has a divisor in the set { 7, 13, 31, 37, 43 }.

Views

Author

Keywords

Comments

Crossrefs

Formula

A244545 Integers n such that for every integer k>0, n*6^k+1 has a divisor in the set { 7, 13, 31, 37, 43 }.

Views

Author

Keywords

Comments

Crossrefs

Formula

A244566 Odd integers n such that for every integer k>0, n*2^k+1 has a divisor in the set { 3, 5, 7, 13, 17, 97, 257 }.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs