A088274 -id:A088274 - cp's OEIS frontend

A101395 Numbers k such that 4*10^k+7 is prime.

0, 1, 3, 9, 39, 2323

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

No further terms < 50000.

a(7) > 2*10^5. - Robert Price May 16 2015

			n = 1, 3, 9 are members since 47, 4007 and 4000000007 are primes.

Makoto Kamada, Prime numbers of the form 400...007.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.
Index entries for primes involving repunits.

Cf. A056806, A100501, A088274, A101714.

Do[ If[ PrimeQ[4*10^n + 7], Print[n]], {n, 0, 10000}]

is(n)=ispseudoprime(4*10^n+7) \\ Charles R Greathouse IV, Jun 12 2017

a(n) = A101714(n-1) + 1.

A102007 Indices of primes in sequence defined by A(0) = 17, A(n) = 10*A(n-1) - 63 for n > 0.

Original entry on oeis.org

0, 1, 3, 7, 8, 23, 59, 109, 133, 221, 411, 699, 998, 1382, 5075, 5542, 6343, 14599, 15092, 21716, 23635, 30220, 50710, 221627, 350070, 371695, 487290, 995255

Offset: 1

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Numbers n such that 10*10^n + 7 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 0 followed by digit 7 is prime.
Numbers corresponding to terms <= 998 are certified primes.
a(24) > 2*10^5. - Robert Price, Nov 09 2015

			10007 is prime, hence 3 is a term.

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Makoto Kamada, Prime numbers of the form 100...007.

Cf. A000533, A002275, A088274.

Select[Range[0, 100000], PrimeQ[10*10^# + 7] &] (* Robert Price, Nov 09 2015 *)

a=17;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-63)

for(n=0,1500,if(isprime(10*10^n+7),print1(n,",")))

a(n) = A088274(n) - 1.

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(24)-a(28) added from A088274 by Amiram Eldar, Nov 28 2021

A107084 Integers k such that 10^k + 33 is prime.

Original entry on oeis.org

1, 3, 6, 9, 10, 31, 47, 70, 281, 366, 519, 532, 775, 1566, 1627, 2247, 2653, 4381, 4571, 7513, 10581, 13239, 15393, 72267, 105515, 215802

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 08 2005

The next term, if it exists, is > 39546. - Robert Price, Aug 21 2010
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10033".
a(26) > 3*10^5. - Robert Price, Oct 26 2023

			For k = 3 we get 10^3 + 33 = 1000 + 33 = 1033, which is prime, so 3 is a term.

Makoto Kamada, Search for 10w33.
Index entries for primes involving repunits.

Cf. A049054, A088274, A088275, A095688, A108052, A108050, A108049, A108054.

a(20)-a(23) from Robert Price, Aug 21 2010
Edited by Ray Chandler, Dec 23 2010
a(24) from Robert Price, Jan 29 2011
a(26) from Robert Price, Oct 26 2023
a(25) from Kamada data by Tyler Busby, Apr 16 2024

A111021 Integers k such that 7*10^k + 31 is a prime number.

Original entry on oeis.org

1, 8, 11, 143, 203, 2727, 2911, 3339, 17039

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "70031".

a(10) > 10^5. - Robert Price, Jan 28 2017

			k = 11 is a term because 7*10^11 + 31 = 7*100000000000 + 31 = 700000000000 + 31 = 700000000031, which is a prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054, A110980.

[n: n in [1..300] | IsPrime(7*10^n+31)]; // Vincenzo Librandi, Jul 03 2016

Select[Range[0, 10000], PrimeQ[7 10^# + 31] &] (* Vincenzo Librandi, Jul 03 2016 *)

a(9) from Ray Chandler, Dec 23 2010

a(1) = 1 prepended by Vincenzo Librandi, Jul 03 2016

A258932 Numbers k such that 10^k + 103 is prime.

Original entry on oeis.org

1, 3, 4, 5, 7, 9, 10, 11, 27, 35, 85, 169, 209, 221, 321, 347, 603, 610, 1229, 1391, 2171, 2303, 2679, 3977, 4545, 5721, 7090, 35877

Offset: 1

Vincenzo Librandi, Jun 15 2015

a(29) > 60000. - Michael S. Branicky, Apr 27 2025

			For n = 3, a(3) = 10^3 + 103 = 1103, which is prime.

Sequences of the type 10^n+k: A049054 (k=3), A088274 (k=7), A088275 (k=9), A095688 (k=13), A108052 (k=19), A108050 (k=21), A108312 (k=27), A107083 (k=31), A107084 (k=33), A135109 (k=37), A135108 (k=39), A108049 (k=43), A108054 (k=49), A135118 (k=51), A135119 (k=57), A135116 (k=61), A135115 (k=63), A135113 (k=67), A135114 (k=69), A135132 (k=73), A135131 (k=79), A137848 (k=81), A135117 (k=87), A110918 (k=91), A135112 (k=93), A135107 (k=97), A110980 (k=99), this sequence (k=103), A258933 (k=109), A165508 (k=111), A248349 (k=123456789), A248351 (k=987654321).

[n: n in [1..600] | IsPrime(10^n+103)];

Select[Range[5000], PrimeQ[10^# + 103] &]

is(n)=ispseudoprime(10^n+103) \\ Charles R Greathouse IV, Jun 13 2017

a(26)-a(28) from Jens Kruse Andersen, Jun 23 2015

A110920 Integers n such that 2*10^n + 81 is a prime number.

Original entry on oeis.org

0, 1, 2, 3, 6, 7, 8, 15, 36, 38, 51, 168, 1000, 2955, 8151, 16456, 17902, 18784, 24948, 28731, 87144

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "20081".

a(22) > 10^5. - Robert Price, Jan 19 2017

			n = 3 is a term because 2*10^3 + 81 = 2*1000 + 81 = 2000 + 81 = 2081 and 2081 is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054.

a(15)-a(18) from Kamada link by Ray Chandler, Dec 23 2010
a(1)-a(2) prepended by Robert Price, Jan 19 2017
a(19)-a(21) from Robert Price, Jan 19 2017

A110933 Integers k such that 3*10^k + 71 is a prime number.

Original entry on oeis.org

1, 4, 7, 16, 19, 190, 227, 235, 283, 319, 1655, 3955, 10666, 30724

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "30071".

a(15) > 10^5. - Robert Price, Jan 22 2017

			k = 7 is a member because: 3*10^7 + 71 = 30000071, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054.

isok(n) = isprime(3*10^n+71); \\ Michel Marcus, Jan 22 2017

a(13) from Ray Chandler, Dec 23 2010
Prepended a(1)=1 by Robert Price, Jan 22 2017
a(14) from Robert Price, Jan 22 2017

A110949 Integers n such that 4*10^n + 61 is prime.

Original entry on oeis.org

1, 2, 7, 11, 191, 248, 1067, 2666, 5252, 13400, 22886, 23739, 29095

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "40061".

a(14) > 10^5. - Robert Price, Jan 22 2017

			n = 7 is in the sequence because 4*10^7 + 61 = 4*10000000 + 61 = 40000000 + 61 = 40000061, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054.

isok(n) = isprime(4*10^n+61); \\ Michel Marcus, Jan 22 2017

a(9)-a(11) from Ray Chandler, Dec 23 2010
Prepended a(1)=1 by Robert Price, Jan 22 2017
a(12)-a(13) from Robert Price, Jan 22 2017

A110983 Integers k such that 5*10^k + 51 is prime.

Original entry on oeis.org

1, 3, 4, 16, 430, 727, 1415, 2691, 3160, 3904, 5464, 19875, 65255, 68524

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "50051".

a(15) > 10^5. - Robert Price, Jan 28 2017

			k = 4 is a member because: 5*10^4+51 = 5*10000+51 = 50000+51 = 50051, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054.

Select[Range[1, 1000], PrimeQ[5*10^# + 51] &] (* Julien Kluge, Dec 15 2016 *)

a(11)-a(12) from Ray Chandler, Dec 23 2010
Prepended a(1)=1 by Robert Price, Jan 28 2017
a(13)-a(14) from Robert Price, Jan 28 2017

A110995 Integers k such that 6*10^k + 41 is a prime number.

Original entry on oeis.org

0, 1, 2, 4, 6, 8, 50, 54, 102, 134, 212, 872, 3055, 3427, 3528, 4262, 4414, 6084, 93792

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "60041".

a(20) > 10^5. - Robert Price, Jan 19 2017

			k = 4 is a term because 6*10^4 + 41 = 6*10000 + 41 = 60000 + 41 = 60041, which is a prime number.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054.

a(18) from Ray Chandler, Dec 23 2010
a(1)-a(2) prepended by Robert Price, Jan 19 2017
a(19) from Robert Price, Jan 19 2017

cp's OEIS Frontend

A101395 Numbers k such that 4*10^k+7 is prime.

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A102007 Indices of primes in sequence defined by A(0) = 17, A(n) = 10*A(n-1) - 63 for n > 0.

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A107084 Integers k such that 10^k + 33 is prime.

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A111021 Integers k such that 7*10^k + 31 is a prime number.

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A258932 Numbers k such that 10^k + 103 is prime.

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PARI

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A110920 Integers n such that 2*10^n + 81 is a prime number.

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A110933 Integers k such that 3*10^k + 71 is a prime number.

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PARI