A244070 -id:A244070 - cp's OEIS frontend

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}.

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.

A244076 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

10157893, 71627707, 86571727, 90109601, 98957849, 99023257, 99284501, 114096371, 142399363, 166262293, 207549337, 213185347, 213708611, 215798563, 229298773, 229306949, 242872709, 251719903, 274263943, 276356999, 278326889, 284716807, 289074853, 294317669

Offset: 1

Pierre CAMI, Jun 19 2014

nonn

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. A076337, A244070, A244071, A244072, A244073, A244074.

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

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.

A243969 Integers n not of form 3m+2 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

9175, 9351, 17676, 24826, 26038, 28612, 38026, 38158, 46212, 46927, 48247, 56473, 61863, 63075, 63898, 65649, 75063, 75195, 83425, 83964, 85284, 91750, 93510, 100935

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+2 then n*10^k+1 is always divisible by 3. The sequence is a base 10 variant of provable Sierpiński numbers (A076336). It is currently unknown whether 7666*10^k+1 is always composite but based on heuristics it probably has large undiscovered primes. 7666 is the only remaining base 10 Sierpiński candidate below 9175. - Jens Kruse Andersen, Jul 09 2014

			9175*10^k+1 is divisible by 11 for k of form 6m+1, 6m+3, 6m+5, by 37 for k of form 6m (and also 6m+3), by 13 for 6m+2, and by 7 for 6m+4. This covers all k. {7, 11, 13, 37} is called a covering set. - _Jens Kruse Andersen_, Jul 09 2014

A. Brunner, C. Caldwell, D. Krywaruczensko, C. Lownsdale, Generalized Sierpiński Numbers Base b (has a typo in covering set for 9175, base 10. - _Jens Kruse Andersen_, Jul 09 2014)

Cf. A076336, A076337, A243974, A244070.

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

Definition corrected by Jens Kruse Andersen, Jul 09 2014

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.

A244348 Integers n such that for every integer k>0, n*10^k+1 has a divisor in the set { 11, 73, 101, 137 }.

Original entry on oeis.org

162207, 1622070, 3349554, 5109589, 6651446, 7001622, 9589051, 10958905, 11273318, 12733181, 14460665, 16220700, 17762557, 18112733, 20700162, 22070016, 22384429, 23844292, 25571776, 27331811, 28873668, 29223844, 31811273, 33181127, 33495540, 34955403, 36682887

Offset: 1

Pierre CAMI, Jun 28 2014

For n > 8, a(n) = a(n-8) + 11111111, the first 8 values are in the data.

If n is of the form 3*m+2, n*10^k+1 is always divisible by 3 but also has a divisor in the set { 11, 73, 101, 137 }.

			Consider n = 162207.
If k is of the form 2*j+1, n*10^(2*j+1)+1 is divisible by 11.
If k is of the form 8*j, n*10^(8*j)+1 is divisible by 137.
If k is of the form 4*j+2, n*10^(4*j+2)+1 is divisible by 101.
If k is of the form 8*j+4 then n*10^(8*j+4)+1 is divisible by 73.
This covers all k, so the covering set is { 11, 73, 101, 137 }.

Robert Israel, Table of n, a(n) for n = 1..10000 (a(1) .. a(27) from _Giovanni Resta_)

Cf. A243974, A244070.

For n > 8, a(n) = a(n-8) + 11111111.

More terms from Giovanni Resta, Nov 23 2019

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.

cp's OEIS Frontend

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}.

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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}.

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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}.

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A244076 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}.

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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}.

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A243969 Integers n not of form 3m+2 such that for any integer k > 0, n*10^k+1 has a divisor in the set { 7, 11, 13, 37 }.

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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 }.

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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 }.

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A244348 Integers n such that for every integer k>0, n*10^k+1 has a divisor in the set { 11, 73, 101, 137 }.

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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 }.

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