A101123 -id:A101123 - 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

A101086 Numbers k for which 997*k + 1009 is prime.

Original entry on oeis.org

0, 6, 10, 12, 22, 36, 64, 76, 82, 94, 126, 130, 136, 144, 150, 162, 174, 186, 202, 204, 246, 250, 252, 274, 276, 292, 294, 300, 306, 312, 330, 342, 360, 364, 390, 430, 466, 472, 480, 484, 490, 502, 526, 540, 546, 582, 586, 592, 594, 606, 610, 616, 622, 642

Offset: 1

Parthasarathy Nambi, Jan 21 2005

nonn

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

			If k=6, then 997*6 + 1009 = 6991 (prime).
If k=10, then 997*10 + 1009 = 10979 (prime).
If k=12, then 997*12 + 1009 = 12973 (prime).

Cf. A100776, A101084, A101123, A101444.

[ n: n in [0..700] | IsPrime(997*n + 1009) ]; // Vincenzo Librandi, Feb 04 2011

Select[Range[0,700],PrimeQ[997#+1009]&] (* Harvey P. Dale, Jun 29 2011 *)

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

A108110 Numbers n such that prime(k)*n+prime(k+1), for k=1,...,6 all are primes.

Original entry on oeis.org

284, 3074, 3494, 21698, 32138, 43874, 51794, 60674, 75494, 407348, 437438, 459794, 571478, 660878, 667358, 705464, 716624, 740774, 811028, 820154, 910664, 1059398, 1077998, 1122584, 1150748, 1210754, 1222898, 1265018, 1412174, 1461164, 1486574, 1585868, 1631438

Offset: 1

Zak Seidov, Jun 03 2005

nonn

n == 0 (mod 2). n == 2 (mod 3). n == 3 or 4 (mod 5). - Jason Yuen, Sep 02 2024

			284 is OK because 2*284+3, 3*284+5, 5*284+7, 7*284+11, 11*284+13 and 13*284+17 all are primes.

Cf. A067076 (k=1), A088879 (k=2), A111224 (k=3), A101123 (k=4), A102721 (k=5).

Cf. A108117 (k=1..7), A379427 (k=1..8).

s={};Do[If[Union[PrimeQ/@Table[Prime[k]*n+Prime[k+1], {k, 6}]]=={True}, s=Append[s, n]], {n, 2, 1000000, 2}];s

\\ See isok from A108117
for(n=1,2*10^6,if(isok(n,6),print1(n", "))) \\ Jason Yuen, Sep 02 2024

a(22)-a(33) from Jason Yuen, Sep 02 2024

A108117 Numbers n such that prime(k)*n+prime(k+1), for k=1,...,7 all are primes.

Original entry on oeis.org

3494, 60674, 75494, 1122584, 2136044, 2473934, 3367244, 5600384, 6629804, 6910784, 7554644, 8572904, 10079144, 11848094, 11892164, 12043214, 12167594, 12269234, 12507284, 12700154, 13459664, 13924544, 14495354, 15005954, 16890914, 17827094, 20642984, 25796054

Offset: 1

Zak Seidov, Jun 03 2005

nonn

The only n, for which also 19*3494+23 is prime, is n=5600384. In principle, n == 4 (mod 10) can give primes of the form prime(k)*n+prime(k+1), for all k from 1 up to 41, while prime(42)*4+prime(43)=181*4+191 == 5 (mod 10) that is nonprime. It'd be very interesting to find at least one n such that prime(k)*n+prime(k+1), k=1,...,41 are all prime.

There are no values of n such that prime(k)*n+prime(k+1), k=1,...,9 are all prime. Proof: If n = 3*i then 2*(3*i)+3 = 3*(2*i+1) is not prime. If n = 3*i+1 then 5*(3*i+1)+7 = 3*(5*i+4) is not prime. If n = 3*i+2 then 23*(3*i+2)+29 = 3*(23*i+25) is not prime. - Jason Yuen, Sep 02 2024

			3494 is OK because 2*3494+3, 3*3494+5, 5*3494+7, 7*3494+11, 11*3494+13, 13*3494+17 and 17*3494+19 all are primes.

Cf. A067076 (k=1), A088879 (k=2), A111224 (k=3), A101123 (k=4), A102721 (k=5), A108976 (k=7).

Cf. A108110 (k=1..6), A379427 (k=1..8).

s={};Do[If[Union[PrimeQ/@Table[Prime[k]*n+Prime[k+1], {k, 7}]]=={True}, s=Append[s, n]], {n, 4, 10000000, 10}];s
Select[Range[9*10^6],AllTrue[Prime[Range[7]]#+Prime[Range[2,8]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 24 2018 *)

isok(n,upto=7)=for(k=1,upto,if(!isprime(prime(k)*n+prime(k+1)),return(0)));1
for(n=1,3*10^7,if(isok(n),print1(n", "))) \\ Jason Yuen, Sep 02 2024

a(13)-a(28) from Jason Yuen, Sep 02 2024

A153350 Numbers n such that 7n+11 is not prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 87, 88, 89

Offset: 1

Vincenzo Librandi, Dec 24 2008

			Distribution of the even terms in the following triangular array:
*;
*,2;
*,*,*;
*,*,*,10;
*,*,*,*,*;
4,*,*,*,*,*;
*,*,*,*,22,*,*;
*,*,*,*,*,30,*,*;
*,12,*,*,*,*,*,*,50;
*,*,*,*,*,*,*,*,*,*;
*,*,*,28,*,*,*,*,*,*,74;
*,*,*,*,*,*,52,*,*,*,*,*;
10,*,*,*,*,*,*,64,*,*,*,*,*; etc.
where * marks the non-integer values of (4*h*k + 2*k + 2*h - 10)/7 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A101123.

[n: n in [0..150] | not IsPrime(7*n+11)]; // VIncenzo Librandi, Jan 13 2013

Select[Range[200], !PrimeQ[7 # + 11] &] (* Vincenzo Librandi, Jan 13 2013 *)

PARI
```
isA153350(n)=!isprime(7*n+11)
```

Corrected and edited by Michael B. Porter, Apr 20 2010

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.

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A101086 Numbers k for which 997*k + 1009 is prime.

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

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

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A108110 Numbers n such that prime(k)*n+prime(k+1), for k=1,...,6 all are primes.

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A108117 Numbers n such that prime(k)*n+prime(k+1), for k=1,...,7 all are primes.

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A153350 Numbers n such that 7n+11 is not prime.

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