A056654 -id:A056654 - cp's OEIS frontend

A257027 Numbers k such that 7R_(k+2) - 610^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 2, 3, 9, 11, 18, 74, 131, 144, 161, 224, 282, 390, 398, 614, 791, 1313, 1866, 9708, 10544, 13292, 13394, 29703, 30779, 72446

Offset: 1

Robert Price, Apr 14 2015

Also, numbers k such that (646*10^k - 7)/9 is prime.
Terms from Kamada.
a(26) > 10^5. Robert Price, Jul 31 2016

			For k=2, 7*R_4 - 6*10^2 = 7777 - 600 = 7177 which is prime.
a(1)=0 associated with 71, a(2)=2 associated with 7177, a(3)=3 associated with 71777, a(4)=9 associated with 71777777777, etc. - _Robert Price_, Jul 31 2016

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 717w.
Index entries for primes involving repunits.

Cf. A002275, A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

[n: n in [0..300] | IsPrime((646*10^n-7) div 9)]; // Vincenzo Librandi, Apr 15 2015

Select[Range[0, 100000], PrimeQ[(646*10^#-7)/9 ] &]

for(n=0,200,if(isprime((646*10^n-7)/9),print1(n,", "))) \\ Derek Orr, Apr 14 2015

a(25) from Robert Price, Jul 31 2016

A262937 Numbers k such that (28*10^k - 13) / 3 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 10, 14, 17, 20, 33, 64, 80, 152, 158, 166, 194, 196, 198, 901, 971, 1289, 1595, 2921, 14390, 28781, 35840

Offset: 1

Robert Price, Sep 23 2016

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 29 is prime (see Example section).

a(28) > 3*10^5.

			2 is in this sequence because (28*10^2 - 13) / 3 = 929 is prime.
Initial terms and associated primes:
a(1) = 0, 5;
a(2) = 1, 89;
a(3) = 2, 929;
a(4) = 4, 93329;
a(5) = 5, 933329, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 93w29.

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

Select[Range[0, 100000], PrimeQ[(28*10^# - 13) / 3] &]

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

A265938 Numbers k such that 6*10^k + 91 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 10, 11, 14, 23, 31, 37, 42, 105, 106, 114, 137, 182, 212, 233, 313, 621, 629, 1067, 1570, 4612, 6288, 20030, 21843, 24800, 43694, 179970

Offset: 1

Robert Price, Apr 06 2016

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 0 followed by the digits 91 is prime (see Example section).

a(34) > 3*10^5.

			3 is in this sequence because 6*10^3+91 = 6091 is prime.
Initial terms and associated primes:
a(1) = 0, 97;
a(2) = 1, 151;
a(3) = 2, 691;
a(4) = 3, 6091;
a(5) = 4, 60091, etc.

Makoto Kamada, Search for 60w91.

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

Select[Range[0, 100000], PrimeQ[6*10^# + 91] &]

is(n)=ispseudoprime(6*10^n + 91) \\ Charles R Greathouse IV, Jun 13 2017

a(33) from Robert Price, May 21 2019

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

Original entry on oeis.org

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

cp's OEIS Frontend

A257027 Numbers k such that 7*R_(k+2) - 6*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

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A262937 Numbers k such that (28*10^k - 13) / 3 is prime.

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A265938 Numbers k such that 6*10^k + 91 is prime.

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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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A257027 Numbers k such that 7R_(k+2) - 610^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.