A268448 -id:A268448 - cp's OEIS frontend

A266582 Numbers k such that (265*10^k - 7)/3 is prime.

1, 2, 4, 9, 13, 14, 16, 46, 99, 112, 116, 127, 146, 208, 512, 848, 1132, 2167, 2482, 2666, 3625, 14410, 16567, 21529, 26272, 69554, 69602

Offset: 1

Robert Price, Jul 10 2016

For k > 0, numbers k such that the digits 88 followed by k-1 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).

a(28) > 10^5.

			4 is in this sequence because (265*10^4 - 7)/3 = 883331 is prime.
Initial terms and associated primes:
a(1) = 1, 881;
a(2) = 2, 8831;
a(3) = 4, 883331l
a(4) = 9, 88333333331;
a(5) = 13, 883333333333331, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 883w1.

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

Select[Range[0, 100000], PrimeQ[(265*10^# - 7)/3] &]

is(n)=ispseudoprime((265*10^n-7)/3) \\ Charles R Greathouse IV, Jun 13 2017

A267865 Numbers k such that 49*10^k + 1 is prime.

Original entry on oeis.org

1, 4, 5, 7, 9, 10, 18, 19, 34, 52, 71, 180, 238, 331, 370, 576, 925, 994, 1075, 1841, 2460, 2857, 6007, 6193, 10836, 18732, 58708, 72861

Offset: 1

Robert Price, Apr 07 2016

Numbers k such that the digits 49 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(29) > 10^5.

			4 is in this sequence because 49*10^4 + 1 = 490001 is prime.
Initial terms and associated primes:
a(1) = 1, 491;
a(2) = 4, 490001;
a(3) = 5, 4900001;
a(4) = 7, 490000001;
a(5) = 9, 49000000001, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 490w1.

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

Select[Range[0, 100000], PrimeQ[49*10^#+1] &]

is(n)=ispseudoprime(49*10^n+1) \\ Charles R Greathouse IV, Jun 13 2017

A269797 Numbers k such that (29*10^k + 91)/3 is prime.

Original entry on oeis.org

1, 2, 3, 4, 8, 11, 18, 27, 39, 54, 55, 65, 75, 83, 111, 164, 189, 191, 204, 252, 322, 371, 449, 646, 678, 754, 1641, 5210, 7787, 11691, 13682, 15994, 22356, 29203, 35756, 57834, 64027, 72985, 74276, 104071, 219124

Offset: 1

Robert Price, Mar 05 2016

For k > 1, numbers k such that digit 9 followed by k-2 occurrences of digit 6 followed by the digits 97 is prime (see Example section).

a(42) > 3*10^5.

			6 is in this sequence because (266*10^n+1)/3 = 88666667 is prime.
Initial terms and associated primes:
a(1) = 1, 127,
a(2) = 2, 997,
a(3) = 3, 9697,
a(4) = 4, 96697,
a(5) = 8, 966666697,
a(6) = 11, 966666666697,
a(7) = 18, 9666666666666666697,
a(8) = 27, 9666666666666666666666666697,
a(9) = 39, 9666666666666666666666666666666666666697, etc.

Makoto Kamada, Search for 96w97.

Cf. A056654, A268448, A269303.

Select[Range[0, 100000], PrimeQ[(29*10^# + 91)/3] &]

isok(n) = isprime((29*10^n + 91)/3); \\ Michel Marcus, Mar 05 2016

a(40) from Robert Price, Apr 12 2020

a(41) from Robert Price, May 31 2023

A270448 Numbers k such that 10^k - 8001 is prime.

Original entry on oeis.org

4, 6, 8, 11, 12, 14, 23, 26, 42, 50, 54, 55, 66, 136, 145, 151, 200, 214, 888, 896, 1674, 2311, 2799, 2836, 2912, 5192, 5907, 8644, 8681, 11914, 18140, 27383, 36549, 57358, 84582, 161253, 167639, 186842, 193230, 204764

Offset: 1

Robert Price, Mar 17 2016

For k > 3, numbers k such that k-4 occurrences of the digit 9 followed by the digits 1999 is prime (see Example section).

a(41) > 3*10^5.

			4 is in this sequence because 10^4-8001 = 1999 is prime.
Initial terms and associated primes:
a(1) = 4, 1999;
a(2) = 6, 991999;
a(3) = 8, 99991999;
a(4) = 11, 99999991999;
a(5) = 12, 999999991999, etc.

Makoto Kamada, Search for 9w1999.

Cf. A056654, A268448, A269303, A270339.

isa := n -> isprime(10^n-8001):
select(isa, [$0..1000]); # Peter Luschny, Jul 22 2019

Select[Range[0, 100000], PrimeQ[10^#-8001 && # > 3] &] (* Corrected by Georg Fischer, Jul 22 2019 *)

isok(n) = isprime(10^n-8001); \\ Michel Marcus, Mar 18 2016

lista(nn) = for(n=1, nn, if(ispseudoprime(10^n-8001), print1(n, ", "))); \\ Altug Alkan, Mar 18 2016

a(36)-a(39) from Robert Price, Mar 27 2018

a(40) from Robert Price, May 31 2023

A270738 Numbers k such that 23*10^k - 7 is prime.

Original entry on oeis.org

1, 2, 3, 6, 8, 12, 18, 19, 30, 65, 77, 126, 353, 541, 576, 723, 777, 1024, 1194, 1507, 2379, 2615, 4008, 4295, 4495, 4526, 9996, 10348, 10673, 14120, 22350, 70240, 93116, 122070, 136225, 183710, 224232, 234025, 270799

Offset: 1

Robert Price, Mar 22 2016

Numbers k such that the digits 22 followed by k-1 occurrences of the digit 9 followed by the digit 3 is prime (see Example section).

a(40) > 3*10^5.

			3 is in this sequence because 23*10^3-7 = 22993 is prime.
Initial terms and associated primes:
a(1) = 1, 223;
a(2) = 2, 2293;
a(3) = 3, 22993;
a(4) = 6, 22999993;
a(5) = 8, 2299999993, etc.

Makoto Kamada, Search for 229w3.

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

Select[Range[0, 100000], PrimeQ[23*10^# - 7] &] (* Corrected by Georg Fischer, Jul 22 2019 *)

lista(nn) = {for(n=1, nn, if(ispseudoprime(23*10^n - 7), print1(n, ", "))); } \\ Altug Alkan, Mar 22 2016

a(34)-a(36) from Robert Price, Feb 25 2020

a(37)-a(39) from Robert Price, May 31 2023

A271107 Numbers k such that 33*10^k + 1 is prime.

Original entry on oeis.org

1, 2, 5, 6, 7, 8, 29, 47, 145, 205, 227, 505, 553, 600, 787, 809, 1305, 1447, 1593, 2285, 4763, 5679, 9133, 12516, 14869, 16536, 33402, 36085, 51933, 56443, 69133

Offset: 1

Robert Price, Mar 30 2016

Numbers k such that the digits 33 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(32) > 10^5.

			5 is in this sequence because 33*10^5+1 = 3300001 is prime.
Initial terms and associated primes:
a(1) = 1, 331;
a(2) = 2, 3301;
a(3) = 5, 3300001;
a(4) = 6, 33000001;
a(5) = 7, 330000001;
a(6) = 8, 3300000001, etc.

Makoto Kamada, Search for 330w1.

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A270974.

Select[Range[0, 100000], PrimeQ[33*10^#+1] &]

lista(nn) = for(n=1, nn, if(ispseudoprime(33*10^n+1), print1(n, ", "))); \\ Altug Alkan, Mar 31 2016

A271146 Numbers k such that (16*10^k - 19)/3 is prime.

Original entry on oeis.org

1, 4, 5, 6, 10, 13, 20, 22, 24, 35, 41, 42, 46, 155, 222, 336, 432, 538, 577, 637, 679, 750, 758, 785, 2262, 5436, 6806, 7962, 9757, 16016, 24588, 47918, 59062, 74092, 81896, 85495, 102299, 185978, 190420

Offset: 1

Robert Price, Mar 31 2016

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 27 is prime (see Example section).

a(40) > 2*10^5.

			4 is in this sequence because (16*10^4 - 19)/3 = 53327 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 4, 53327;
a(3) = 5, 533327;
a(4) = 6, 5333327;
a(5) = 10, 53333333327;
a(6) = 13, 53333333333327, etc.

Makoto Kamada, Search for 53w27.

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A270974.

Select[Range[0, 100000], PrimeQ[(16*10^# - 19)/3] &]

lista(nn) = {for(n=1, nn, if(ispseudoprime((16*10^n - 19)/3), print1(n, ", ")));} \\ Altug Alkan, Mar 31 2016

a(37)-a(39) from Robert Price, Feb 23 2019

A271147 Numbers k such that (28*10^k + 113)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 9, 12, 16, 22, 23, 42, 52, 57, 63, 117, 119, 208, 266, 324, 481, 779, 1244, 1289, 2998, 5522, 5599, 5771, 6820, 12367, 14737, 22612, 30623, 31596, 58956, 59133, 138240, 163709, 250655, 259897

Offset: 1

Robert Price, Mar 31 2016

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 71 is prime (see Example section).

a(41) > 3*10^5.

			3 is in this sequence because (28*10^3+113)/3 = 9371 is prime.
Initial terms and associated primes:
a(1) = 0, 47;
a(2) = 1, 131;
a(3) = 2, 971;
a(4) = 3, 9371;
a(5) = 4, 93371;
a(6) = 6, 9333371, etc.

Makoto Kamada, Search for 93w71.

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

Select[Range[0, 100000], PrimeQ[(28*10^# + 113)/3] &]

is(n)=ispseudoprime((28*10^n + 113)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(37)-a(38) from Robert Price, Mar 13 2020

a(39)-a(40) from Robert Price, Jun 17 2023

A271340 Numbers k such that (14*10^k + 73)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 10, 15, 19, 32, 54, 68, 114, 148, 227, 238, 286, 405, 789, 857, 1310, 2314, 3613, 4103, 4215, 5135, 6094, 8023, 8718, 16899, 34215, 41989, 81585, 85010, 143097, 165282, 199447

Offset: 1

Robert Price, Apr 05 2016

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 6 followed by the digits 91 is prime (see Example section).

a(39) > 2*10^5.

			3 is in this sequence because (14*10^3 + 73)/3 = 4691 is prime.
Initial terms and associated primes:
a(1) = 0, 29;
a(2) = 1, 71;
a(3) = 2, 491;
a(4) = 3, 4691;
a(5) = 4, 46691;
a(6) = 6, 4666691, etc.

Makoto Kamada, Search for 46w91.

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271109, A271269.

Select[Range[0, 100000], PrimeQ[(14*10^# + 73)/3] &]

is(n)=ispseudoprime((14*10^n + 73)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(36)-a(38) from Robert Price, Dec 26 2018

A271360 Numbers k such that 5*10^k + 87 is prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 16, 38, 39, 46, 61, 62, 100, 116, 152, 190, 298, 472, 642, 688, 1676, 1971, 2338, 4389, 4520, 4986, 7765, 9428, 10820, 18984, 19797, 35360, 42146, 168807

Offset: 1

Robert Price, Apr 05 2016

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 87 is prime (see Example section).

a(34) > 2*10^5.

			3 is in this sequence because 5*10^3 + 87 = 5087 is prime.
Initial terms and associated primes:
a(1) = 1, 137;
a(2) = 2, 587;
a(3) = 3, 5087;
a(4) = 4, 50087;
a(5) = 6, 5000087, etc.

Makoto Kamada, Search for 50w87.

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

Select[Range[0, 100000], PrimeQ[5*10^# + 87] &]

is(n)=ispseudoprime(5*10^n + 87) \\ Charles R Greathouse IV, Jun 13 2017

a(33) from Robert Price, Feb 24 2019

cp's OEIS Frontend

A266582 Numbers k such that (265*10^k - 7)/3 is prime.

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A267865 Numbers k such that 49*10^k + 1 is prime.

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A269797 Numbers k such that (29*10^k + 91)/3 is prime.

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A270448 Numbers k such that 10^k - 8001 is prime.

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A270738 Numbers k such that 23*10^k - 7 is prime.

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A271107 Numbers k such that 33*10^k + 1 is prime.

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A271146 Numbers k such that (16*10^k - 19)/3 is prime.

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