A101086 -id:A101086 - cp's OEIS frontend

A101448 Nonnegative numbers k such that 2k + 11 is prime.

0, 1, 3, 4, 6, 9, 10, 13, 15, 16, 18, 21, 24, 25, 28, 30, 31, 34, 36, 39, 43, 45, 46, 48, 49, 51, 58, 60, 63, 64, 69, 70, 73, 76, 78, 81, 84, 85, 90, 91, 93, 94, 100, 106, 108, 109, 111, 114, 115, 120, 123, 126, 129, 130, 133, 135, 136, 141, 148, 150, 151, 153, 160, 163

Offset: 1

Parthasarathy Nambi, Jan 24 2005

2 is the smallest single-digit prime and 11 is the smallest two-digit prime.

			If n=1, then 2*1 + 11 = 13 (prime).
If n=49, then 2*49 + 11 = 109 (prime).
If n=69, then 2*69 + 11 = 149 (prime).

Shawn A. Broyles, Table of n, a(n) for n = 1..1000

Cf. A101123, A101086.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), this seq (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

Filtered([0..200], k-> IsPrime(2*k+11) ); # G. C. Greubel, May 21 2019

[n: n in [0..200] | IsPrime(2*n+11)]; // Vincenzo Librandi, Nov 17 2010

select(k-> isprime(11+2*k), [$0..200])[];  # Alois P. Heinz, Jun 02 2022

Select[Range[0, 200], PrimeQ[2# + 11] &] (* Stefan Steinerberger, Feb 28 2006 *)

is(n)=isprime(2*n+11) \\ Charles R Greathouse IV, Apr 29 2015

[n for n in (0..200) if is_prime(2*n+11) ] # G. C. Greubel, May 21 2019

More terms from Stefan Steinerberger, Feb 28 2006

Definition clarified by Zak Seidov, Jul 11 2014

A101123 Numbers k for which 7*k + 11 is prime.

Original entry on oeis.org

0, 6, 8, 14, 18, 20, 24, 26, 36, 38, 48, 54, 60, 68, 78, 80, 84, 86, 90, 96, 104, 114, 116, 128, 138, 140, 144, 146, 150, 156, 158, 168, 170, 174, 188, 204, 206, 210, 216, 224, 228, 230, 236, 246, 248, 254, 260, 266, 270, 284, 288, 294, 296, 300, 306, 318, 320

Offset: 1

Parthasarathy Nambi, Jan 21 2005

nonn

Note that 7 is the largest single-digit prime and 11 is the smallest two-digit prime.

			For k=6, 7*6 + 11 = 53 (prime).
For k=8, 7*8 + 11 = 67 (prime).
For k=14, 7*14 + 11 = 109 (prime).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A017029, A101084, A101086, A101444.

Select[Range[0,500],PrimeQ[7#+11]&] (* Harvey P. Dale, Jun 05 2012 *)

isA101123(n)=isprime(7*n+11) \\ Michael B. Porter, Apr 20 2010

Extended by Ray Chandler, Jan 25 2005

A101084 Numbers k such that 97*k + 101 is a prime.

Original entry on oeis.org

0, 6, 8, 14, 18, 30, 36, 50, 86, 90, 96, 110, 114, 116, 126, 128, 134, 138, 140, 156, 158, 174, 186, 194, 200, 204, 218, 236, 258, 260, 266, 278, 294, 296, 300, 314, 326, 336, 338, 344, 348, 354, 366, 368, 378, 398, 420, 428, 468, 470, 476, 498, 504, 516, 524

Offset: 1

Parthasarathy Nambi, Jan 21 2005

nonn

97 is the largest two-digit prime and 101 is the smallest three-digit prime.

			If k=6, then 97*6 + 101 = 683 (prime).
If k=8, then 97*8 + 101 = 877 (prime).
If k=14, then 97*14 + 101 = 1459 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A100775, A101086, A101123, A101444.

[ n: n in [0..600] | IsPrime(97*n+101) ]; // Vincenzo Librandi, Feb 04 2011

Extended by Ray Chandler, Jan 25 2005

A101444 Numbers k such that (9973*k + 10007) is a prime.

Original entry on oeis.org

0, 14, 32, 42, 48, 98, 104, 108, 120, 122, 132, 180, 204, 210, 224, 228, 230, 264, 278, 300, 302, 308, 318, 342, 344, 348, 350, 374, 384, 402, 410, 414, 428, 438, 444, 462, 470, 500, 522, 540, 564, 602, 614, 638, 644, 672, 678, 692, 698, 714, 720, 740, 782

Offset: 1

Parthasarathy Nambi, Jan 18 2005

nonn

Note that 9973 is the largest four-digit prime and 10007 is the smallest five-digit prime.

			If k=14 then 9973*14 + 10007 = 149629 (prime).
If k=32 then 9973*32 + 10007 = 329143 (prime).
If k=42 then 9973*42 + 10007 = 428873 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A101123, A101084, A101086, A101442.

Select[ Range[ 0, 791], PrimeQ[9973# + 10007]&] (* Robert G. Wilson v, Jan 20 2005 *)

Extended by Lior Manor, Ray Chandler and Robert G. Wilson v, Jan 20 2005

A100776 a(n) = 997*n + 1009.

Original entry on oeis.org

1009, 2006, 3003, 4000, 4997, 5994, 6991, 7988, 8985, 9982, 10979, 11976, 12973, 13970, 14967, 15964, 16961, 17958, 18955, 19952, 20949, 21946, 22943, 23940, 24937, 25934, 26931, 27928, 28925, 29922, 30919, 31916, 32913, 33910, 34907, 35904, 36901, 37898, 38895

Offset: 0

Parthasarathy Nambi, Jan 03 2005

Note that 997 is the largest three-digit prime and 1009 is the smallest four-digit prime.

			If n=1, 997*1 + 1009 = 2006.
If n=2, 997*2 + 1009 = 3003.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A017029, A100775, A101086, A101442.

[997 * n + 1009: n in [0..50]]; // Vincenzo Librandi, Jul 14 2011

A100776:=n->997 * n + 1009; seq(A100776(n), n=0..50); # Wesley Ivan Hurt, Jan 22 2014

Table[997 n + 1009, {n, 0, 50}] (* Wesley Ivan Hurt, Jan 22 2014 *)

a(n)=997*n+1009 \\ Charles R Greathouse IV, Jul 10 2016

From Elmo R. Oliveira, Dec 07 2024: (Start)
G.f.: (1009 - 12*x)/(1 - x)^2.
E.g.f.: (1009 + 997*x)*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005

Edited by Ray Chandler, Jan 25 2005

A108341 Numbers n such that 997*n - 1009 is prime.

Original entry on oeis.org

6, 8, 18, 30, 36, 38, 44, 66, 78, 90, 98, 104, 116, 134, 140, 144, 156, 164, 168, 170, 200, 228, 230, 246, 248, 260, 276, 296, 318, 344, 354, 374, 378, 380, 386, 408, 420, 426, 450, 464, 468, 480, 500, 510, 546, 576, 578, 584, 606, 608, 618, 620, 630, 654, 678

Offset: 1

Parthasarathy Nambi, Jun 30 2005

997 and 1009 are primes.

All terms are even. - Harvey P. Dale, Mar 09 2019

			If n=6, then 997*n - 1009 = 4973 (prime).
If n=90, then 997*n - 1009 = 88721 (prime).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A101086.

a:=proc(n) if isprime(997*n-1009)=true then n else fi end: seq(a(n),n=1..750); # Emeric Deutsch, Jul 04 2005

Select[Range[2,700,2],PrimeQ[997#-1009]&] (* Harvey P. Dale, Mar 09 2019 *)

is(n)=isprime(997*n-1009) \\ Charles R Greathouse IV, Jun 13 2017

More terms from Emeric Deutsch, Jul 04 2005

A101503 Numbers k such that 11*k + 101 is prime.

Original entry on oeis.org

0, 6, 10, 12, 16, 28, 30, 40, 42, 46, 52, 58, 60, 66, 76, 88, 90, 100, 102, 108, 118, 126, 130, 132, 136, 138, 142, 160, 168, 172, 180, 192, 208, 210, 216, 220, 222, 228, 238, 240, 250, 256, 258, 268, 276, 280, 282, 292, 306, 310, 312, 322, 328, 336, 342, 346

Offset: 1

Parthasarathy Nambi, Jan 24 2005

11 is the smallest two-digit prime and 101 is the smallest three-digit prime.

			If k=0, then 11*0 + 101 = 101 (prime).
If k=6, then 11*6 + 101 = 167 (prime).
If k=60, then 11*60 + 101 = 761 (prime).

Cf. A101123, A101086.

[n: n in [0..1000] | IsPrime(11*n + 101)]; // Vincenzo Librandi, Nov 17 2010

Select[Range[0, 300], PrimeQ[11# + 101] &] (* Stefan Steinerberger, Feb 28 2006 *)

is(n)=isprime(11*n+101) \\ Charles R Greathouse IV, Jun 13 2017

More terms from Stefan Steinerberger, Feb 28 2006

cp's OEIS Frontend

A101448 Nonnegative numbers k such that 2k + 11 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Extensions

A101123 Numbers k for which 7*k + 11 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A101084 Numbers k such that 97*k + 101 is a prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Extensions

A101444 Numbers k such that (9973*k + 10007) is a prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A100776 a(n) = 997*n + 1009.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

Extensions

A108341 Numbers n such that 997*n - 1009 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

A101503 Numbers k such that 11*k + 101 is prime.