A111094 -id:A111094 - cp's OEIS frontend

A153400 Numbers n such that 18*n+1 is not prime.

0, 3, 5, 8, 12, 13, 14, 16, 18, 19, 20, 23, 25, 26, 28, 31, 33, 36, 37, 38, 39, 40, 43, 44, 47, 48, 50, 53, 54, 57, 58, 60, 61, 63, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 80, 82, 83, 84, 88, 89, 91, 93, 95, 96, 98

Offset: 1

Vincenzo Librandi, Dec 25 2008

			Distribution of the positive terms in the following triangular array:
*;
*,*;
*,*,*;
*,*,*,*;
*,3,*,*,*;
*,*,5,*,*,*;
*,*,*,*,*,*,*;
*,*,*,*,*,*,*,16;
*,*,*,*,*,*,*,*,20;
*,*,*,*,*,*,*,*,*,*;
*,*,*,*,14,*,*,*,*,*,*; etc.
where * marks the noninteger values of (2*h*k + k + h)/9 with h >= k >= 1. - _Vincenzo Librandi_, Jan 14 2013

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

Cf. A111094.

[n: n in [0..150] | not IsPrime(18*n+1)]; // Vincenzo Librandi, Jan 14 2013

Select[Range[0, 200], !PrimeQ[18 # + 1] &] (* Vincenzo Librandi, Jan 14 2013 *)

0 added by Arkadiusz Wesolowski, Aug 03 2011

A165810 Primes p such that 18*p+1 is also a prime.

Original entry on oeis.org

2, 7, 11, 17, 29, 41, 59, 71, 79, 97, 127, 137, 139, 149, 151, 181, 197, 199, 241, 251, 277, 281, 307, 337, 347, 367, 379, 401, 431, 479, 491, 541, 569, 587, 659, 701, 709, 757, 797, 809, 821, 827, 829, 857, 877, 881, 947, 991, 1021, 1051, 1109, 1117, 1129, 1151, 1229

Offset: 1

Vincenzo Librandi, Sep 28 2009

			For p=2, 18*p+1=37. For p=7, 18*p+1=127. For p=11, 18*p+1=199.

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

Cf. A111094, A153400, A165811.

Select[Prime[Range[1000]],PrimeQ[18#+1]&]  (* Harvey P. Dale, Mar 06 2011 *)

a(n) = (A165811(n)-1)/18.

Extended by R. J. Mathar, Oct 16 2009

A165811 Primes of the form 18*p+1, where p is also a prime.

Original entry on oeis.org

37, 127, 199, 307, 523, 739, 1063, 1279, 1423, 1747, 2287, 2467, 2503, 2683, 2719, 3259, 3547, 3583, 4339, 4519, 4987, 5059, 5527, 6067, 6247, 6607, 6823, 7219, 7759, 8623, 8839, 9739, 10243, 10567, 11863, 12619, 12763, 13627, 14347, 14563, 14779, 14887

Offset: 1

Vincenzo Librandi, Sep 28 2009

			p=2 contributes 37=18*2+1. p=7 contributes 127=18*7+1. p=11 contributes 199=18*11+1

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

Cf. A111094, A153400, A165810.

[a: p in PrimesInInterval(2, 1000) | IsPrime(a) where a is 18*p + 1]; // Vincenzo Librandi, Oct 13 2012

Select[Table[18p + 1, {p, Prime[Range[400]]}], PrimeQ] (* Vincenzo Librandi, Oct 13 2012 *)

a(n) = 1+18*A165810(n).

Extended by R. J. Mathar, Oct 16 2009

A098877 Least k such that 3(6n)^k + 1 is prime.

Original entry on oeis.org

1, 1, 3, 1, 3, 1, 1, 3, 1, 1, 1, 14, 2, 2, 1, 3, 1, 270, 12, 2, 1, 1, 8, 1, 3, 2, 1, 2, 1, 1, 12, 1, 11, 1, 1, 2, 2, 12, 3, 2, 1, 1, 8, 2, 1, 1, 2, 3, 1, 2, 1, 1, 11, 3, 1, 1, 14, 2, 1, 16, 24, 1, 4, 1, 1, 3, 9, 3, 66, 4, 1, 1, 3, 6, 3, 3, 2, 7, 1, 3, 1, 156, 3, 2, 1, 1, 1, 12, 77, 1, 5, 1, 20, 1, 3, 2

Offset: 1

Pierre CAMI, Oct 13 2004

nonn

Cf. A098876, A111094.

f[n_] := Block[{k = 1}, While[ !PrimeQ[3*((6*n)^k) + 1], k++ ]; k]; Table[ f[n], {n, 96}] (* Robert G. Wilson v, Oct 21 2004 *)

a(A111094(n)) = 1. - Michel Marcus, Jul 28 2015

More terms from Robert G. Wilson v, Oct 21 2004

cp's OEIS Frontend

A153400 Numbers n such that 18*n+1 is not prime.

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A165810 Primes p such that 18*p+1 is also a prime.

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A165811 Primes of the form 18*p+1, where p is also a prime.

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Author

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Examples

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Crossrefs

Programs

Magma

Mathematica

Formula

Extensions

A098877 Least k such that 3*(6*n)^k + 1 is prime.

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Author

Keywords

Crossrefs

Programs

Mathematica

Formula

Extensions

A098877 Least k such that 3(6n)^k + 1 is prime.