A271269 -id:A271269 - cp's OEIS frontend

A272929 Numbers k such that (8*10^k - 77)/3 is prime.

2, 4, 5, 6, 15, 18, 43, 45, 55, 60, 105, 128, 180, 207, 271, 479, 869, 1220, 1478, 1937, 4003, 4213, 5503, 9562, 11388, 13120, 34049, 47178, 156371, 271039

Offset: 1

Robert Price, May 10 2016

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

a(31) > 3*10^5.

			4 is in this sequence because (8*10^4 - 77)/3 = 26641 is prime.
Initial terms and associated primes:
a(1) = 2, 241;
a(2) = 4, 26641;
a(3) = 5, 266641;
a(4) = 6, 2666641;
a(5) = 15, 2666666666666641, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 26w41.

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

Select[Range[1, 100000], PrimeQ[(8*10^# - 77)/3] &]

lista(nn) = {for(n=1, nn, if(ispseudoprime((8*10^n - 77)/3), print1(n, ", ")));} \\ Altug Alkan, May 11 2016

a(29) from Robert Price, Jul 07 2018

a(30) from Robert Price, Jul 02 2023

A272999 Numbers k such that (11*10^k + 49)/3 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 10, 11, 16, 18, 21, 22, 30, 41, 69, 83, 128, 166, 190, 262, 263, 353, 496, 1398, 1793, 2806, 9722, 15733, 32420, 61095, 77909, 110496

Offset: 1

Robert Price, May 12 2016

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 83 is prime (see Example section).

a(32) > 3*10^5.

			4 is in this sequence because (11*10^4 + 49)/3 = 36683 is prime.
Initial terms and associated primes:
a(1) = 1, 53;
a(2) = 2, 383:
a(3) = 4, 36683;
a(4) = 5, 366683;
a(5) = 7, 36666683, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 36w83.

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

Select[Range[0, 100000], PrimeQ[(11*10^# + 49)/3] &]

is(n)=ispseudoprime((11*10^n + 49)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(31) from Robert Price, Jul 19 2018

A273006 Numbers k such that 88*10^k + 3 is prime.

Original entry on oeis.org

1, 2, 3, 7, 19, 21, 31, 50, 55, 151, 167, 287, 542, 603, 926, 1046, 2066, 2139, 2651, 2787, 5756, 6028, 6925, 10135, 13037, 36476, 74234, 119295

Offset: 1

Robert Price, Nov 09 2016

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

a(29) > 3*10^5.

			3 is in this sequence because 88*10^3 + 3 = 88003 is prime.
Initial terms and associated primes:
a(1) = 1, 883;
a(2) = 2, 8803;
a(3) = 3, 88003;
a(4) = 7, 880000003;
a(5) = 19, 880000000000000000003, etc.

Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 880w3.

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

Select[Range[0, 100000], PrimeQ[88*10^# + 3] &] (* Corrected by Georg Fischer, Jul 22 2019 *)

is(n)=ispseudoprime(88*10^n + 3) \\ Charles R Greathouse IV, Jun 13 2017

a(28) from Robert Price, May 03 2020

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

Original entry on oeis.org

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

cp's OEIS Frontend

A272929 Numbers k such that (8*10^k - 77)/3 is prime.

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A272999 Numbers k such that (11*10^k + 49)/3 is prime.

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A273006 Numbers k such that 88*10^k + 3 is prime.

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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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