A088878 -id:A088878 - cp's OEIS frontend

A136060 Daughter primes of order 11.

3, 7, 13, 31, 37, 43, 61, 73, 103, 163, 211, 223, 241, 271, 307, 313, 331, 367, 397, 421, 463, 523, 541, 577, 643, 727, 757, 853, 877, 883, 937, 1051, 1087, 1093, 1153, 1237, 1291, 1303, 1381, 1423, 1471, 1597, 1693, 1723, 1777, 1951, 1993, 2131, 2161, 2203

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest daughter primes of order n see A136019 (also definition). For daughter primes of order 1 see A088878. For daughter primes of order 2 see A136051. For daughter primes of order 3 see A136052. For daughter primes of order 4 see A136053. For daughter primes of order 5 see A136054. For daughter primes of order 6 see A136055. For daughter primes of order 7 see A136056. For daughter primes of order 8 see A136057. For daughter primes of order 9 see A136058. For daughter primes of order 10 see A136059.

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

Cf. A088878, A091180, A136019, A136020, A136051, A136052, A136053, A136054, A136055, A136056, A136057, A136058, A136059.

n = 11; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, (Prime[k] + 2n)/(2n + 1)]], {k, 1, 1500}]; a

A136063 Mother primes of order 4.

Original entry on oeis.org

19, 37, 109, 163, 199, 271, 379, 523, 541, 631, 739, 919, 1009, 1171, 1459, 1549, 1621, 1783, 1999, 2053, 2089, 2143, 2161, 2251, 2521, 2539, 2791, 2971, 3169, 3673, 3889, 3943, 4159, 4483, 4519, 4861, 5059, 5113, 5563, 5779, 5869, 5923, 6211, 6301, 6373

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062.

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

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136064, A136065, A136066, A136067, A136068, A136069, A136070.

n = 4; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136064 Mother primes of order 5.

Original entry on oeis.org

23, 67, 199, 331, 397, 463, 661, 727, 859, 1123, 1783, 2113, 2179, 2311, 2971, 3037, 3433, 3631, 3697, 4027, 4093, 4159, 4357, 4621, 5347, 5479, 5743, 6007, 6271, 6337, 6733, 7393, 7591, 7789, 8053, 8317, 8647, 9043, 9109, 9439, 9967, 10099, 10627

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063.

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

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136065, A136066, A136067, A136068, A136069, A136070.

n = 5; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136065 Mother primes of order 6.

Original entry on oeis.org

53, 79, 131, 157, 521, 547, 599, 677, 859, 911, 937, 1249, 1301, 1327, 1951, 2029, 2237, 2341, 2549, 2731, 2887, 2939, 3121, 3251, 3329, 3407, 3511, 3797, 4057, 4759, 4967, 5591, 5981, 6007, 6761, 7229, 7307, 7411, 7489, 7879, 8009, 8191, 8581, 8737

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064.

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

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136066, A136067, A136068, A136069, A136070.

n = 6; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136067 Mother primes of order 8.

Original entry on oeis.org

103, 307, 613, 1021, 1123, 1327, 2143, 2347, 2551, 3061, 3571, 3877, 4591, 6427, 6733, 7753, 8263, 8467, 9181, 9283, 10303, 10711, 11731, 12037, 12343, 12547, 12853, 15607, 15913, 16831, 17137, 17341, 17851, 18973, 19891, 21013, 21727

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064. For mother primes of order 6 see A136065. For mother primes of order 8 see A136066.

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

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136065, A136066, A136068, A136069, A136070.

n = 8; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136068 Mother primes of order 9.

Original entry on oeis.org

191, 229, 419, 571, 761, 1103, 1483, 1559, 1901, 2053, 2129, 2851, 3079, 4219, 4409, 4523, 4561, 4751, 6271, 6689, 6803, 7069, 7753, 8171, 8209, 8513, 8741, 8779, 9311, 9463, 9539, 10831, 11743, 11971, 12161, 12503, 12541, 12959, 14251, 14593, 14669

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064. For mother primes of order 6 see A136065. For mother primes of order 8 see A136066. For mother primes of order 9 see A136067.

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

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136065, A136066, A136067, A136069, A136070.

n = 9; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136070 Mother primes of order 11.

Original entry on oeis.org

47, 139, 277, 691, 829, 967, 1381, 1657, 2347, 3727, 4831, 5107, 5521, 6211, 7039, 7177, 7591, 8419, 9109, 9661, 10627, 12007, 12421, 13249, 14767, 16699, 17389, 19597, 20149, 20287, 21529, 24151, 24979, 25117, 26497, 28429, 29671, 29947

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064. For mother primes of order 6 see A136065. For mother primes of order 8 see A136066. For mother primes of order 9 see A136067. For mother primes of order 10 see A136068.

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

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136065, A136066, A136067, A136068, A136069.

n = 11; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A259730 Primes p such that both 2p - 3 and 3p - 2 are prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 23, 37, 43, 53, 67, 71, 113, 127, 137, 167, 181, 191, 193, 211, 251, 263, 331, 347, 373, 431, 433, 443, 461, 487, 587, 727, 751, 757, 907, 991, 1021, 1091, 1103, 1171, 1187, 1213, 1231, 1297, 1367, 1453, 1483, 1597, 1637, 1663, 1667, 1733

Offset: 1

Reinhard Zumkeller, Jul 05 2015

nonn

A010051(2*a(n) - 3) * A010051(3*a(n) - 2) = 1;
A259758(n) = (2*a(n) - 3) * (3*a(n) - 2).
Except for a(1)=3 this is the same sequence as primes p such that A288814(3*p) - A288814(2*p) = 5. - David James Sycamore, Jul 22 2017
Furthermore, (A288814(3*p)*A288814(2*p))/6 belongs to A259758. - David James Sycamore, Jul 23 2017

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Intersection of A063908 and A088878; A172287, A259758.

Cf. A288814, A259758.

import Data.List.Ordered (isect)
a259730 n = a259730_list !! (n-1)
a259730_list = a063908_list `isect` a088878_list

Select[Prime@ Range@ 270, Times @@ Boole@ Map[PrimeQ, {2 # - 3, 3 # - 2}] > 0 &] (* Michael De Vlieger, Jul 22 2017 *)
Select[Prime[Range[300]],AllTrue[{2#-3,3#-2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 08 2020 *)

lista(nn) = forprime(p=3, nn, if(isprime(2*p-3) && isprime(3*p-2), print1(p, ", "))); \\ Altug Alkan, Jul 22 2017

A172287 Primes p such that exactly one of 2p-3 and 3p-2 is prime.

Original entry on oeis.org

17, 31, 41, 47, 61, 83, 97, 101, 103, 107, 157, 163, 223, 233, 241, 257, 271, 277, 283, 293, 307, 311, 313, 317, 337, 401, 421, 457, 467, 491, 521, 523, 541, 547, 557, 563, 577, 593, 601, 613, 617, 631, 641, 643, 647, 653, 661, 673, 677, 701, 743, 761, 773

Offset: 1

Juri-Stepan Gerasimov, Jan 30 2010

A010051(2*a(n)+3) + A010051(3*a(n)+2) = 1; each term is either a term of A063908 or of A088878. - Reinhard Zumkeller, Jul 02 2015

No terms end in 9. Dickson's conjecture implies that there are infinitely many terms. - Robert Israel, Jul 02 2015

			a(1)=17 because 2*17-3=31 is prime and 3*17-2=49 is nonprime.
19 is not a term because neither 2*19-3=35 nor 3*19-2=55 is prime;
23 is not a term because both 2*23-3=43 and 3*23-2=67 are prime.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000040, A010051, A063908, A088878, A259730.

a172287 n = a172287_list !! (n-1)
a172287_list = filter
   (\p -> a010051' (2 * p - 3) + a010051' (3 * p - 2) == 1) a000040_list
-- Reinhard Zumkeller, Jul 02 2015

A172287:=n->`if`(isprime(n) and (isprime(2*n-3) xor isprime(3*n-2)), n, NULL): seq(A172287(n), n=1..1000); # Wesley Ivan Hurt, Jun 23 2015

Select[Prime@ Range@ 150, Xor[PrimeQ[2 # - 3], PrimeQ[3 # - 2]] &] (* Michael De Vlieger, Jul 01 2015 *)

Extended by Charles R Greathouse IV, Mar 25 2010

A153184 Numbers n such that 3*n-2 is not prime.

Original entry on oeis.org

1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 17, 18, 19, 20, 22, 24, 26, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 54, 56, 57, 58, 59, 60, 62, 63, 64, 66, 68, 69, 70, 72, 73, 74, 76, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 94, 96, 97, 98, 99, 100

Offset: 1

Vincenzo Librandi, Dec 20 2008

One more than the associated value in A153309. - R. J. Mathar, Jan 05 2011

			Distribution of the odd terms > a(1) in the following triangular array:
*;
*,9;
*,*,17;
*,*,*,*;
*,19,*,*,41;
*,*,31,*,*,57;
*,*,*,*,*,*,*;
*,29,*,*,63,*,*,97;
*,*,45,*,*,83,*,*,121;
*,*, *,*,*,*, *,*, *, *;
*,39,*,*,85,*,*,131,*,*,177;
*,*,59,*,*,109,*,*,159,*,*,209; etc.
where * marks the non-integer values of (4*h*k + 2*k + 2*h + 3)/3 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013

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

Cf. A153183, A088878.

[n: n in [0..120] | not IsPrime(3*n - 2)]; // Vincenzo Librandi, Jan 12 2013

lst={};Do[If[ !PrimeQ[3*n-2],AppendTo[lst,n]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 22 2008 *)
Select[Range[0, 100], !PrimeQ[3 # - 2] &] (* Vincenzo Librandi, Jan 12 2013 *)

is(n)=!isprime(3*n-2) \\ Charles R Greathouse IV, Oct 26 2015

a(n) ~ n. - Charles R Greathouse IV, Oct 26 2015

Erroneous comment deleted by N. J. A. Sloane, Jun 23 2010

cp's OEIS Frontend

A136060 Daughter primes of order 11.

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A136063 Mother primes of order 4.

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A136064 Mother primes of order 5.

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A136065 Mother primes of order 6.

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A136067 Mother primes of order 8.

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A136068 Mother primes of order 9.

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A136070 Mother primes of order 11.

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A259730 Primes p such that both 2*p - 3 and 3*p - 2 are prime.

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Haskell

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PARI

A172287 Primes p such that exactly one of 2p-3 and 3p-2 is prime.

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A259730 Primes p such that both 2p - 3 and 3p - 2 are prime.