A268448 -id:A268448 - cp's OEIS frontend

A269303 Numbers k such that (266*10^k + 1)/3 is prime.

0, 1, 2, 3, 4, 5, 6, 8, 10, 13, 19, 26, 37, 69, 77, 81, 214, 242, 255, 900, 1113, 1833, 3166, 3566, 4753, 4849, 4869, 5005, 7372, 7702, 10240, 16100, 18972, 28574, 33815, 37820, 70457, 89482, 106066, 133603, 154897, 278325

Offset: 1

Robert Price, Feb 22 2016

For k > 0, numbers k such that digits 88 followed by k-1 occurrences of digit 6 followed by the digit 7 is prime (see Example section).

a(43) > 3*10^5.

			6 is in this sequence because (266*10^n+1)/3 = 88666667 is prime.
Initial terms and associated primes:
a(1)  = 0,    89;
a(2)  = 1,    887;
a(3)  = 2,    8867;
a(4)  = 3,    88667;
a(5)  = 4,    886667;
a(6)  = 5,    8866667;
a(7)  = 6,    88666667;
a(8)  = 8,    8866666667;
a(9)  = 10,   886666666667;
a(10) = 13,   886666666666667, etc.

Makoto Kamada, Search for 886w7.

Cf. A056654, A268448.

[n: n in [0..220] | IsPrime((266*10^n + 1) div 3)]; // Vincenzo Librandi, Feb 23 2016

Select[Range[0, 100000], PrimeQ[(266*10^#+1)/3] &]

is(n)=ispseudoprime((266*10^n + 1)/3) \\ Charles R Greathouse IV, Feb 16 2017

a(39)-a(41) from Robert Price, Apr 22 2020

a(42) from Robert Price, May 31 2023

A270339 Numbers k such that (11*10^k + 19)/3 is prime.

Original entry on oeis.org

1, 2, 3, 9, 17, 18, 20, 24, 29, 36, 48, 114, 126, 135, 153, 170, 241, 363, 483, 579, 681, 948, 2483, 2798, 3081, 5137, 5640, 6890, 7080, 12600, 16929, 24253, 24793, 35546, 52956, 69645, 133831, 206688

Offset: 1

Robert Price, Mar 15 2016

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 73 is prime (see Example section).

a(39) > 3*10^5.

			3 is in this sequence because (11*10^3 + 19)/3 = 3673 is prime.
Initial terms and associated primes:
a(1) = 1, 43;
a(2) = 2, 373;
a(3) = 3, 3673;
a(4) = 9, 3666666673;
a(5) = 17, 366666666666666673, etc.

Makoto Kamada, Search for 36w73.

Cf. A056654, A268448, A269303.

Select[Range[0, 100000], PrimeQ[(11*10^# + 19)/3] &]

is(n)=isprime((11*10^n + 19)/3) \\ Charles R Greathouse IV, Mar 16 2016

a(37) from Robert Price, Sep 16 2018

a(38) from Robert Price, Jul 25 2024

A270613 Numbers k such that (68*10^k + 7)/3 is prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 10, 24, 25, 29, 34, 35, 37, 46, 49, 88, 103, 290, 381, 484, 696, 751, 886, 999, 1750, 5062, 6214, 9740, 12558, 16551, 24674, 28600, 37427, 48032, 61991, 70148, 72516, 99441, 179656

Offset: 1

Robert Price, Mar 20 2016

Numbers k such that the digits 22 followed by k-1 occurrences of the digit 6 followed by the digit 9 is prime (see Example section).

a(39) > 3*10^5.

			3 is in this sequence because (68*10^3+7)/3 = 22669 is prime.
Initial terms and associated primes:
a(1) = 1, 229;
a(2) = 2, 2269;
a(3) = 3, 22669;
a(4) = 4, 226669;
a(5) = 7, 226666669, etc.

Makoto Kamada, Search for 226w9.

Cf. A056654, A268448, A269303, A270339.

Select[Range[0, 100000], PrimeQ[(68*10^# + 7)/3] &]

lista(nn) = for(n=1, nn, if(ispseudoprime((68*10^n + 7)/3), print1(n, ", "))); \\ Altug Alkan, Mar 20 2016

a(38) from Robert Price, Jan 16 2020

A270831 Numbers k such that (7*10^k + 71)/3 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 23, 29, 37, 39, 40, 89, 115, 189, 227, 253, 301, 449, 533, 607, 969, 1036, 1207, 1407, 1701, 3493, 7147, 11342, 21638, 22327, 25575, 25648, 34079, 39974, 47719, 49913, 74729, 100737, 103531, 168067

Offset: 1

Robert Price, Mar 23 2016

nonn

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 57 is prime (see Example section).

a(41) > 2*10^5.

			3 is in this sequence because (7*10^3 + 71)/3 = 2357 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 2, 257;
a(3) = 3, 2357;
a(4) = 4, 23357;
a(5) = 5, 233357, etc.

Makoto Kamada, Search for 23w57.

Cf. A056654, A268448, A269303, A270339, A270613.

Select[Range[0, 100000], PrimeQ[(7*10^# + 71)/3] &]

lista(nn) = {for(n=1, nn, if(ispseudoprime((7*10^n + 71)/3), print1(n, ", "))); } \\ Altug Alkan, Mar 23 2016

a(38)-a(40) from Robert Price, May 21 2018

A270890 Numbers k such that (8*10^k + 49)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 10, 24, 33, 34, 35, 45, 52, 56, 62, 65, 103, 166, 424, 886, 1418, 1825, 4895, 5715, 7011, 7810, 9097, 12773, 14746, 20085, 25359, 27967, 46629, 48507, 68722, 74944, 102541, 118960, 157368

Offset: 1

Robert Price, Mar 25 2016

For k > 2, numbers k such that the digit 2 followed by k-3 occurrences of the digit 6 followed by the digits 83 is prime (see Example section).

a(41) > 3*10^5.

			3 is in this sequence because (8*10^3 + 49)/3 = 2683 is prime.
Initial terms and associated primes:
a(1) = 0, 19;
a(2) = 1, 43;
a(3) = 2, 283;
a(4) = 3, 2683;
a(5) = 4, 26683;
a(6) = 5, 266683, etc.

Makoto Kamada, Search for 26w83.

Cf. A056654, A268448, A269303, A270339, A270613, A270831.

Select[Range[0, 100000], PrimeQ[(8*10^# + 49)/3] &]

is(n)=isprime((8*10^n + 49)/3) \\ Charles R Greathouse IV, Feb 16 2017

a(38)-a(40) from Robert Price, May 23 2020

A270929 Numbers k such that (16*10^k - 31)/3 is prime.

Original entry on oeis.org

1, 2, 3, 4, 15, 20, 24, 32, 38, 40, 63, 93, 104, 194, 208, 514, 535, 600, 928, 1300, 1485, 1780, 2058, 3060, 3356, 3721, 6662, 11552, 15482, 23000, 27375, 34748, 57219, 61251, 85221, 99656, 103214, 103244, 276537

Offset: 1

Robert Price, Mar 26 2016

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 23 is prime (see Example section).

a(40) > 3*10^5. - Robert Price, Jul 13 2023

			3 is in this sequence because (16*10^3 - 31)/3 = 5323 is prime.
Initial terms and associated primes:
a(1) = 1, 43;
a(2) = 2, 523;
a(3) = 3, 5323;
a(4) = 4, 53323;
a(5) = 15, 5333333333333323;
a(6) = 20, 533333333333333333323, etc.

Makoto Kamada, Search for 53w23.

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890.

Select[Range[0, 100000], PrimeQ[(16*10^# - 31)/3] &]

isok(n) = ispseudoprime((16*10^n - 31)/3); \\ Michel Marcus, Mar 26 2016

a(37)-a(38) from Robert Price, Mar 03 2019

a(39) from Robert Price, Jul 13 2023

A271269 Numbers k such that 8*10^k - 49 is prime.

Original entry on oeis.org

1, 2, 3, 8, 24, 49, 57, 74, 104, 131, 144, 162, 182, 246, 302, 352, 557, 581, 589, 704, 939, 1181, 1937, 2157, 4463, 6013, 7266, 8504, 8691, 16129, 20108, 40677, 74234, 112018

Offset: 1

Robert Price, Apr 03 2016

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 9 followed by the digits 51 is prime (see Example section).

a(35) > 2*10^5.

			3 is in this sequence because 8*10^3 - 49 = 7951 is prime.
Initial terms and associated primes:
a(1) = 1, 31;
a(2) = 2, 751;
a(3) = 3, 7951;
a(4) = 8, 799999951;
a(6) = 24, 7999999999999999999999951, etc.

Makoto Kamada, Search for 79w51.

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929.

Select[Range[0, 100000], PrimeQ[8*10^# - 49] &]

is(n)=isprime(8*10^n - 49) \\ Charles R Greathouse IV, Feb 16 2017

a(34) from Robert Price, Aug 20 2019

A270974 Numbers k such that 7*10^k + 57 is prime.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 12, 14, 19, 21, 27, 33, 60, 61, 91, 102, 535, 549, 614, 695, 709, 1014, 2448, 2519, 3464, 3511, 6348, 6841, 11009, 11177, 20754, 26610, 30651, 39246, 122294

Offset: 1

Robert Price, Mar 27 2016

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 0 followed by the digits 57 is prime (see Example section).

a(35) > 2*10^5.

			3 is in this sequence because 7*10^3+57 = 7057 is prime.
Initial terms and associated primes:
a(1) = 1, 127;
a(2) = 2, 757;
a(3) = 3, 7057;
a(4) = 5, 700057;
a(5) = 6, 7000057;
a(6) = 7, 70000057, etc.

Makoto Kamada, Search for 70w57.

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929.

[n: n in [1..500] | IsPrime(7*10^n + 57)]; // Vincenzo Librandi, Jul 03 2016

Select[Range[0, 100000], PrimeQ[7*10^# + 57] &]

lista(nn) = {for(n=1, nn, if(ispseudoprime(7*10^n + 57), print1(n, ", ")));} \\ Altug Alkan, Mar 27 2016

a(35) from Robert Price, Jun 13 2019

A254441 Numbers k such that (41*10^k + 49)/9 is prime.

Original entry on oeis.org

2, 3, 6, 20, 26, 38, 51, 119, 155, 218, 446, 486, 1211, 1319, 1338, 1365, 1575, 5106, 7019, 9503, 9695, 14304, 15417, 17765, 24222, 25500, 26306, 35238, 93207

Offset: 1

Robert Price, Apr 17 2016

For terms k > 1, numbers that begin with the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 61 are prime (see Example section).

a(30) > 2*10^5.

			3 is in this sequence because (41*10^3 + 49)/9 = 4561 is prime.
Initial terms and associated primes:
a(1) = 2, 461;
a(2) = 3, 4561;
a(3) = 6, 4555561;
a(4) = 20, 455555555555555555561;
a(5) = 26, 455555555555555555555555561, etc.

Alois P. Heinz, Table of n, a(n) for n = 1..29
Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 45w61.

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Select[Range[0, 100000], PrimeQ[(41*10^# + 49)/9] &]

is(n)=ispseudoprime((41*10^n + 49)/9) \\ Charles R Greathouse IV, Jun 13 2017

A271109 Numbers k such that (5 * 10^k - 119)/3 is prime.

Original entry on oeis.org

2, 3, 5, 6, 8, 11, 26, 33, 35, 41, 69, 73, 204, 230, 295, 381, 392, 537, 776, 1187, 2187, 2426, 4182, 4589, 5841, 6107, 11513, 13431, 28901, 56256, 65203, 66613, 82085, 91707, 126871, 140281

Offset: 1

Robert Price, Apr 05 2016

For k > 1, numbers k such that the digit 1 followed by k - 2 occurrences of the digit 6 followed by the digits 27 is prime (see Example section).

a(37) > 2*10^5.

			3 is in this sequence because (5*10^3 - 119)/3 = 1627 is prime.
Initial terms and associated primes:
a(1) = 2, 127;
a(2) = 3, 1627;
a(3) = 5, 166627;
a(4) = 6, 1666627;
a(5) = 8, 166666627, etc.

Makoto Kamada, Search for 16w27.

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Select[Range[10^5], PrimeQ[(5 * 10^# - 119)/3] &]

is(n)=ispseudoprime((5*10^n-119)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(35)-a(36) from Robert Price, Mar 29 2018

cp's OEIS Frontend

A269303 Numbers k such that (266*10^k + 1)/3 is prime.

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A270339 Numbers k such that (11*10^k + 19)/3 is prime.

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A270613 Numbers k such that (68*10^k + 7)/3 is prime.

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A270831 Numbers k such that (7*10^k + 71)/3 is prime.

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A270890 Numbers k such that (8*10^k + 49)/3 is prime.

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A270929 Numbers k such that (16*10^k - 31)/3 is prime.

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A271269 Numbers k such that 8*10^k - 49 is prime.

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