A270831 -id:A270831 - cp's OEIS frontend

A273042 Numbers k such that (28*10^k + 191)/3 is prime.

0, 1, 2, 3, 5, 6, 9, 10, 33, 49, 92, 109, 548, 757, 814, 1289, 1460, 1644, 2782, 6355, 8028, 9276, 9366, 9765, 12002, 12089, 14491, 16180, 29102, 30989, 151682, 183403, 190105, 253210

Offset: 1

Robert Price, May 13 2016

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).

a(35) > 3*10^5.

			3 is in this sequence because (28*10^3 + 191)/3 = 9397 is prime.
Initial terms and associated primes:
a(1) = 0, 73;
a(2) = 1, 157:
a(3) = 2, 997;
a(4) = 3, 9397;
a(5) = 5, 933397, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 93w97.

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

Select[Range[0, 100000], PrimeQ[(28*10^# + 191)/3] &]

is(n)=ispseudoprime((28*10^n + 191)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(31)-a(33) from Robert Price, Feb 27 2020

a(34) from Robert Price, Jul 12 2023

A273063 Numbers k such that (112*10^k + 17)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 44, 53, 79, 89, 95, 120, 224, 259, 290, 488, 725, 821, 1815, 3096, 3100, 3404, 5909, 8054, 11879, 17298, 25588, 41516, 127324, 191900

Offset: 1

Robert Price, May 14 2016

For k > 0, numbers k such that the digits 37 followed by k-1 occurrences of the digit 3 followed by the digit 9 is prime (see Example section).

a(31) > 3*10^5.

			3 is in this sequence because (112*10^3+17)/3 = 37339 is prime.
Initial terms and associated primes:
a(1) = 0, 43;
a(2) = 1, 379:
a(3) = 2, 3739;
a(4) = 3, 37339;
a(5) = 4, 373339, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 373w9.

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

Select[Range[0, 100000], PrimeQ[(112*10^# + 17)/3] &]

is(n)=ispseudoprime((112*10^n + 17)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(29)-a(30) from Robert Price, Mar 05 2020

A273097 Numbers k such that 4*10^k + 87 is prime.

Original entry on oeis.org

1, 2, 4, 5, 13, 25, 27, 32, 37, 38, 40, 45, 57, 80, 91, 151, 214, 441, 644, 764, 797, 1222, 2329, 2931, 4324, 21794, 22396, 24041, 46420, 51489, 55165, 126625

Offset: 1

Robert Price, May 15 2016

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 87 is prime (see Example section).

a(33) > 3*10^5.

			4 is in this sequence because 4*10^4 + 87 = 40087 is prime.
Initial terms and associated primes:
a(1) = 1, 127:
a(2) = 2, 487;
a(3) = 4, 40087;
a(4) = 5, 400087;
a(5) = 13, 40000000000087, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 40w87.

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

Select[Range[0, 100000], PrimeQ[4*10^# + 87] &]

is(n)=ispseudoprime(4*10^n + 87) \\ Charles R Greathouse IV, Jun 13 2017

a(32) from Robert Price, Aug 15 2018

A273265 Numbers k such that (16*10^k + 161)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 6, 7, 8, 10, 16, 17, 35, 53, 121, 155, 178, 487, 880, 1153, 2136, 2790, 2803, 5775, 5845, 5971, 7131, 13213, 13813, 17153, 31461, 38735, 93577, 188457

Offset: 1

Robert Price, May 18 2016

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 87 is prime (see Example section).

a(33) > 2*10^5.

			3 is in this sequence because (16*10^3 + 161)/3 = 5387 is prime.
Initial terms and associated primes:
a(1) = 0, 59;
a(2) = 1, 107;
a(3) = 2, 587;
a(4) = 3, 5387;
a(5) = 6, 5333387, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 53w87.

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

Select[Range[0, 100000], PrimeQ[(16*10^# + 161)/3] &]

is(n)=ispseudoprime((16*10^n + 161)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(32) from Robert Price, Feb 27 2019

A273371 Numbers k such that (17*10^k - 77)/3 is prime.

Original entry on oeis.org

1, 2, 3, 6, 9, 15, 21, 26, 33, 42, 131, 168, 434, 464, 501, 1004, 1011, 1089, 1509, 2025, 2283, 2526, 9150, 9464, 14139, 14827, 18941, 32426, 36719, 42933, 138569

Offset: 1

Robert Price, May 20 2016

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 41 is prime (see Example section).

a(32) > 3*10^5.

			3 is in this sequence because (17*10^3-77)/3 = 5641 is prime.
Initial terms and associated primes:
a(1) = 1, 31;
a(2) = 2, 541;
a(3) = 3, 5641;
a(4) = 6, 5666641;
a(5) = 9, 5666666641, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 56w41.

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

Select[Range[0, 100000], PrimeQ[(17*10^# - 77)/3] &]

is(n)=ispseudoprime((17*10^n - 77)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(31) from Robert Price, Aug 21 2019

A273542 Numbers k such that (238*10^k - 1)/3 is prime.

Original entry on oeis.org

0, 2, 3, 4, 6, 10, 12, 38, 40, 47, 59, 76, 131, 154, 227, 404, 762, 782, 987, 993, 3449, 5692, 10086, 11630, 15135, 26384, 28233, 33179, 48352, 103210, 118265, 145276, 151979, 209715, 210712

Offset: 1

Robert Price, May 24 2016

For k > 1, numbers k such that the digits 79 followed by k occurrences of the digit 3 is prime (see Example section).

a(36) > 3*10^5.

			3 is in this sequence because (238*10^3-1)/3 = 79333 is prime.
Initial terms and associated primes:
a(1) = 0, 79;
a(2) = 2, 7933;
a(3) = 3, 79333;
a(4) = 4, 793333;
a(5) = 6, 79333333, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 793w.

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

[n: n in [0..500] | IsPrime((238*10^n - 1) div 3)]; // Vincenzo Librandi, May 25 2016

Select[Range[0, 100000], PrimeQ[(238*10^# - 1)/3] &]

is(n)=ispseudoprime(238*10^n\3) \\ Charles R Greathouse IV, Jun 08 2016

a(30)-a(33) from Robert Price, Apr 01 2020

a(34)-a(35) from Robert Price, Oct 26 2023

A273679 Numbers k such that 10^k - 1000000001 is prime.

Original entry on oeis.org

11, 18, 22, 26, 27, 36, 45, 59, 140, 162, 201, 278, 427, 563, 588, 757, 951, 2006, 3938, 4127, 4490, 5637, 6074, 6725, 7025, 10191, 25628, 39415, 51872, 57501, 90227, 115773, 117142, 148934

Offset: 1

Robert Price, May 27 2016

For k > 9, numbers k such that k-10 occurrences of the digit 9 followed by the digits 8999999999 is prime (see Example section).

a(35) > 2*10^5.

			11 is in this sequence because 10^11 - 1000000001 = 98999999999 is prime.
Initial terms and associated primes:
a(1) = 11, 98999999999,
a(2) = 18, 999999998999999999,
a(3) = 22, 9999999999998999999999,
a(4) = 26, 99999999999999998999999999,
a(5) = 27, 999999999999999998999999999, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 9w8999999999.

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

Select[Range[0, 100000], PrimeQ[10^#-1000000001] &]

is(n)=ispseudoprime(10^n-10^9-1) \\ Charles R Greathouse IV, Jun 08 2016

from sympy import isprime
def afind(limit):
    tenk = 10**10
    for k in range(10, limit+1):
        if isprime(tenk - 1000000001): print(k, end=", ")
        tenk *= 10
afind(100000) # Michael S. Branicky, Nov 18 2021

a(32)-a(33) from Robert Price, Mar 01 2018

a(34) from Robert Price, Dec 31 2020

A273726 Numbers k such that (25*10^k + 59)/3 is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 26, 52, 75, 97, 98, 160, 227, 295, 413, 686, 901, 975, 1088, 1481, 2555, 4001, 4361, 5637, 7568, 8641, 19526, 26633, 92186

Offset: 1

Robert Price, May 28 2016

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 53 is prime (see Example section).

a(29) > 2*10^5.

			3 is in this sequence because (25*10^3+59)/3 = 8353 is prime.
Initial terms and associated primes:
a(1) = 1, 103;
a(2) = 2, 853;
a(3) = 3, 8353;
a(4) = 5, 833353;
a(5) = 6, 83333353, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 83w53.

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

Select[Range[0, 100000], PrimeQ[(25*10^# + 59)/3] &]

is(n)=ispseudoprime((25*10^n + 59)/3) \\ Charles R Greathouse IV, Jun 08 2016

A273728 Numbers k such that (17*10^k + 79)/3 is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 12, 37, 45, 55, 139, 205, 264, 445, 975, 1111, 1298, 1340, 1835, 2264, 2317, 2897, 2955, 3001, 4134, 6637, 7063, 20613, 114795, 147890

Offset: 1

Robert Price, May 28 2016

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 93 is prime (see Example section).

a(30) > 3*10^5. - Robert Price, Jul 10 2023

			3 is in this sequence because (17*10^3+79)/3 = 5693 is prime.
Initial terms and associated primes:
a(1) = 1, 83;
a(2) = 2, 593;
a(3) = 3, 5693;
a(4) = 5, 566693;
a(5) = 7, 56666693, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 56w93.

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

Select[Range[0, 100000], PrimeQ[(17*10^# + 79)/3] &]

is(n)=ispseudoprime((17*10^n + 79)/3) \\ Charles R Greathouse IV, Jun 08 2016

a(28)-a(29) from Robert Price, Apr 15 2019

A273783 Numbers k such that (86*10^k - 77)/9 is prime.

Original entry on oeis.org

2, 3, 8, 9, 12, 14, 27, 32, 50, 80, 98, 99, 194, 237, 338, 828, 830, 1265, 2583, 3639, 5232, 5940, 9371, 10268, 13424, 26975, 36147, 60165, 69260, 93263

Offset: 1

Robert Price, May 30 2016

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 5 followed by the digits 47 is prime (see Example section).

a(31) > 2*10^5.

			3 is in this sequence because (86*10^3 - 77)/9 = 9547 is prime.
Initial terms and associated primes:
a(1) = 2, 947;
a(2) = 3, 9547;
a(3) = 8, 955555547;
a(4) = 9, 9555555547;
a(5) = 12, 9555555555547, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 95w47.

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

Select[Range[0, 100000], PrimeQ[(86*10^# - 77)/9] &]

is(n)=ispseudoprime((86*10^n - 77)/9) \\ Charles R Greathouse IV, Jun 08 2016

cp's OEIS Frontend

A273042 Numbers k such that (28*10^k + 191)/3 is prime.

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A273063 Numbers k such that (112*10^k + 17)/3 is prime.

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A273097 Numbers k such that 4*10^k + 87 is prime.

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A273265 Numbers k such that (16*10^k + 161)/3 is prime.

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A273371 Numbers k such that (17*10^k - 77)/3 is prime.

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A273542 Numbers k such that (238*10^k - 1)/3 is prime.

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Magma

Mathematica

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A273679 Numbers k such that 10^k - 1000000001 is prime.

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