A110801 -id:A110801 - cp's OEIS frontend

A111174 Numbers k such that 24*k + 1 is prime.

3, 4, 8, 10, 13, 14, 17, 18, 19, 24, 25, 28, 32, 39, 42, 43, 47, 48, 50, 52, 54, 55, 62, 67, 69, 73, 74, 75, 78, 83, 84, 87, 88, 89, 90, 95, 99, 103, 105, 108, 109, 112, 113, 118, 119, 123, 125, 127, 130, 132, 134, 138, 140, 143, 144, 147, 153, 154, 157, 158, 162

Offset: 1

Parthasarathy Nambi, Oct 21 2005

nonn

Half of the even terms in A110801. - R. J. Mathar, Jan 31 2011

			If k=99 then 24*k + 1 = 2377 (prime).

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

Cf. A153384 (complement), A107008 (conjecturally equivalent)

[ n: n in [0..1500] | IsPrime(24*n + 1) ]; // Vincenzo Librandi, Jan 31 2011

Select[Range[200],PrimeQ[24#+1]&] (* Harvey P. Dale, Apr 01 2018 *)

is(n)=isprime(24*n+1) \\ Charles R Greathouse IV, Feb 20 2017

More terms from Christian G. Bower, Jan 06 2006

A124411 Numbers k such that 2k+1, 4k+1, 6k+1, 8k+1, 10k+1 and 12k+1 are primes.

Original entry on oeis.org

12705, 13020, 105525, 256410, 966840, 1707510, 1944495, 2310000, 2478630, 3132675, 3836070, 3976770, 4112430, 4532325, 5499585, 5920005, 6610485, 7390845, 8552250, 10739505, 11120340, 12231450, 12338130, 13243230, 16467255

Offset: 1

Artur Jasinski, Oct 31 2006

nonn

Jinyuan Wang, Table of n, a(n) for n = 1..100

Cf. A005097, A005098, A024899, A005123, A024912, A110801, A123998, A124408, A124409, A124410, A071576.

Select[Range[10^7], And @@ PrimeQ /@ ({2, 4, 6, 8, 10, 12}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)

is(k) = sum(j = 1, 6, isprime(2*j*k+1)) == 6; \\ Jinyuan Wang, Aug 04 2019

Extended by Ray Chandler, Nov 20 2006

A167055 Numbers k such that 12*k + 5 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 9, 11, 12, 14, 16, 19, 21, 22, 23, 24, 26, 29, 32, 33, 37, 38, 42, 43, 46, 47, 49, 51, 53, 54, 56, 58, 63, 64, 66, 67, 68, 71, 73, 77, 78, 79, 81, 84, 87, 88, 91, 92, 98, 99, 101, 102, 106, 107, 108, 113, 114, 117, 119, 123, 124, 129, 133, 134, 136, 141

Offset: 1

Michael B. Porter, Oct 27 2009

Corresponds to odd numbers in A024898.

			2 is in the sequence since 12*2+5 = 29 is prime.

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

Cf. A110801, A167056, A167057, A024898, primes are in A040117.

[n: n in [1..150] | IsPrime(12*n+5)]; // Vincenzo Librandi, May 20 2014

Select[Range[0,150],PrimeQ[12#+5]&] (* Harvey P. Dale, Oct 07 2012 *)

PARI
```
isA167055(n) = isprime(12*n+5)
```

A167056 Numbers k such that 12*k + 7 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 8, 10, 11, 12, 13, 16, 17, 18, 22, 23, 25, 27, 30, 31, 36, 38, 40, 41, 43, 45, 47, 50, 51, 52, 53, 57, 60, 61, 62, 65, 67, 68, 71, 73, 75, 76, 80, 82, 86, 87, 88, 90, 93, 97, 102, 106, 107, 108, 110, 116, 118, 120, 121, 122, 123, 127, 128, 130, 131, 135, 138

Offset: 1

Michael B. Porter, Oct 27 2009

Corresponds to odd numbers in A024899.

			2 is in the sequence since 12*2+7 = 31 is prime.

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

A110801, A167055, A167057, A024899, primes are in A068229.

[n: n in [1..150] | IsPrime(12*n+7)]; // Vincenzo Librandi, May 20 2014

Select[Range[0, 200], PrimeQ[12 # + 7] &] (* Vincenzo Librandi, May 20 2014 *)

PARI
```
isA167056(n) = isprime(12*n+7)
```

A167057 Numbers k such that 12*k + 11 is prime.

Original entry on oeis.org

0, 1, 3, 4, 5, 6, 8, 10, 13, 14, 15, 18, 19, 20, 21, 25, 28, 29, 31, 34, 35, 36, 38, 39, 40, 41, 46, 48, 49, 53, 54, 56, 59, 61, 68, 69, 71, 73, 75, 78, 80, 81, 84, 85, 90, 91, 95, 96, 98, 101, 104, 106, 108, 109, 113, 118, 119, 120, 123, 124, 125, 126, 129, 130, 131, 133

Offset: 1

Michael B. Porter, Oct 27 2009

Corresponds to even numbers in A024898.

			3 is in the sequence since 12*3+11 = 47 is prime.

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

Cf. A110801, A167055, A167056, A024898, primes are in A068231.

[n: n in [0..200] |IsPrime(12*n+11)]; // Vincenzo Librandi, Mar 25 2010

Select[Range[0, 200], PrimeQ[12 # + 11] &] (* Vincenzo Librandi, May 20 2014 *)

PARI
```
isA167057(n) = isprime(12*n+11)
```

a(n) = A138620(n)-1. [From R. J. Mathar, Oct 29 2009]

A123985 Numbers n for which 12n+1, 12n+5, 12n+7 and 12n+11 are primes.

Original entry on oeis.org

1, 3, 8, 38, 71, 73, 108, 166, 288, 376, 656, 871, 1156, 1338, 1618, 1751, 1776, 1856, 1921, 1963, 2311, 2418, 2801, 3501, 3538, 3648, 3818, 4266, 4541, 4611, 4651, 5076, 6723, 6751, 7388, 7533, 7621, 7698, 7738, 7796, 8083, 8193, 9073, 9243, 9418, 9516

Offset: 1

Artur Jasinski, Oct 30 2006

nonn

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A110801.

Select[Range[10^4], And @@ PrimeQ /@ ({1, 5, 7, 11} + 12#) &] (* Ray Chandler, Nov 22 2006 *)

P=isprime;
for(n=0, 10^5, if(P(12*n+1) && P(12*n+5) && P(12*n+7) && P(12*n+11), print1(n", ")));
\\ Joerg Arndt, Jul 11 2014

A153383 Numbers n such that 12*n+1 is not prime.

Original entry on oeis.org

0, 2, 4, 7, 10, 11, 12, 14, 17, 18, 21, 22, 24, 25, 27, 30, 32, 37, 39, 40, 41, 42, 43, 44, 46, 47, 49, 52, 53, 54, 57, 58, 60, 62, 65, 66, 67, 68, 70, 72, 74, 75, 76, 77, 79, 80, 81, 82, 87, 88, 90, 92, 95, 97, 98, 99, 102, 105, 106, 107, 109, 111, 112, 113, 114

Offset: 1

Vincenzo Librandi, Dec 25 2008

Complement of A110801 (12*n+1 is prime). [Klaus Brockhaus, Jan 02 2009]

			Triangle begins:
*;
*,2;
*,*,4;
*,*,*,*;
*,*,*,*,10;
*,*,*,*,*,14;
*,*,*,*,*,*,*:
*,7,*,*,*,*,*,24;
*,*,11,*,*,*,*,*,30;
where * marks the non-integer values of (2*h*k + k + h)/6 with h >= k >= 1.- _Vincenzo Librandi_, Jan 13 2013

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

Cf. A110801.

[ n: n in [0..120] | not IsPrime(12*n+1) ]; // Klaus Brockhaus, Jan 02 2009

Select[Range[0, 200], !PrimeQ[12*# + 1] &] (* Vincenzo Librandi, Jan 13 2013 *)

More terms from Klaus Brockhaus, Jan 02 2009

0 added by Arkadiusz Wesolowski, Aug 03 2011

A123979 Numbers k such that 12k+1, 12k+5 and 12*k+7 are primes.

Original entry on oeis.org

1, 3, 8, 16, 23, 38, 51, 71, 73, 108, 141, 156, 166, 178, 198, 233, 271, 288, 346, 376, 451, 453, 471, 478, 646, 656, 773, 778, 786, 871, 926, 1003, 1013, 1031, 1156, 1213, 1311, 1338, 1543, 1576, 1618, 1696, 1751, 1776, 1793, 1846, 1856, 1921, 1933, 1963

Offset: 1

Artur Jasinski, Oct 30 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A110801.

a:=proc(n) if isprime(12*n+1)=true and isprime(12*n+5)=true and isprime(12*n+7)=true then n else fi end: seq(a(n),n=1..2800); # Emeric Deutsch, Nov 06 2006

Select[Range[2000], And @@ PrimeQ /@ ({1, 5, 7} + 12#) &] (* Ray Chandler, Nov 05 2006 *)

Extended by Ray Chandler, Nov 05 2006

More terms from Emeric Deutsch, Nov 06 2006

A255218 Numbers k such that 12k+1, 24k+1, 36k+1 and 72k+1 are all prime.

Original entry on oeis.org

28, 103, 190, 253, 355, 848, 1328, 1783, 1898, 1958, 1988, 2170, 2213, 3003, 3533, 3808, 3913, 3988, 4450, 4488, 4593, 4800, 5460, 5808, 5853, 6448, 6545, 6903, 7103, 7238, 7295, 7400, 7483, 7693, 8533, 9310, 9780, 10260, 10885, 12185, 12628, 15513, 16163

Offset: 1

Vincenzo Librandi, Feb 26 2015

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
Umberto Cerruti, Pseudoprimi di Fermat e numeri di Carmichael (in Italian), p. 14.

Subsequence of A110801 and A111174.

Cf. A255578.

[n: n in [0..20000] | IsPrime(12*n+1) and IsPrime(24*n+1) and IsPrime(36*n+1) and IsPrime(72*n+1)];

[n: n in [0..20000] | forall{i: i in Divisors(6) | IsPrime(12*i*n+1)}];

Select[Range[10000], PrimeQ[12 # + 1] && PrimeQ[24 # + 1] && PrimeQ[36 # + 1] && PrimeQ[72 # + 1] &]
Select[Range[17000],AllTrue[{12,24,36,72}#+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 16 2016 *)

A123982 Numbers k such that 12k+1, 12k+5 and 12*k+11 are primes.

Original entry on oeis.org

1, 3, 8, 19, 29, 38, 56, 71, 73, 78, 84, 91, 101, 108, 119, 124, 129, 133, 134, 166, 199, 203, 224, 236, 246, 288, 294, 301, 316, 344, 376, 399, 411, 423, 488, 623, 628, 631, 656, 686, 724, 728, 819, 861, 871, 883, 894, 1008, 1009, 1053, 1074, 1086, 1156, 1179

Offset: 1

Artur Jasinski, Oct 30 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A110801.

a:=proc(n) if isprime(12*n+1)=true and isprime(12*n+5)=true and isprime(12*n+11)=true then n else fi end: seq(a(n),n=1..1400); # Emeric Deutsch, Nov 06 2006

Select[Range[1200], And @@ PrimeQ /@ ({1, 5, 11} + 12#) &] (* Ray Chandler, Nov 05 2006 *)

Extended by Ray Chandler, Nov 05 2006

More terms from Emeric Deutsch, Nov 06 2006

cp's OEIS Frontend

A111174 Numbers k such that 24*k + 1 is prime.

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A124411 Numbers k such that 2k+1, 4k+1, 6k+1, 8k+1, 10k+1 and 12k+1 are primes.

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A167055 Numbers k such that 12*k + 5 is prime.

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A167056 Numbers k such that 12*k + 7 is prime.

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Magma

Mathematica

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A167057 Numbers k such that 12*k + 11 is prime.

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A123985 Numbers n for which 12n+1, 12n+5, 12n+7 and 12n+11 are primes.

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Mathematica

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A153383 Numbers n such that 12*n+1 is not prime.

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Magma

A123979 Numbers k such that 12k+1, 12k+5 and 12*k+7 are primes.

A255218 Numbers k such that 12k+1, 24k+1, 36k+1 and 72k+1 are all prime.

A123982 Numbers k such that 12k+1, 12k+5 and 12*k+11 are primes.