A136083 -id:A136083 - cp's OEIS frontend

A023208 Primes p such that 3*p + 2 is also prime.

3, 5, 7, 13, 17, 19, 23, 29, 37, 43, 59, 79, 83, 89, 97, 103, 127, 139, 149, 163, 167, 173, 197, 199, 227, 233, 239, 257, 269, 293, 313, 317, 337, 349, 353, 367, 383, 397, 409, 419, 433, 439, 457, 479, 499, 503, 523, 569, 577, 607, 643, 659, 709, 757, 769, 797, 859, 863

Offset: 1

David W. Wilson

Also, son primes of order 1. For smallest son primes of order n see A136027 (also definition). For son primes of order 2 see A136082. - Artur Jasinski, Dec 12 2007

Zak Seidov and Michael De Vlieger, Table of n, a(n) for n = 1..10000 (first 1000 terms from _Zak Seidov_)
Rosemary Sullivan and Neil Watling, Independent divisibility pairs on the set of integers from 1 to n, INTEGERS 13 (2013) #A65.

Cf. A023208, A094524, A136019, A136020, A136026, A136027, A136082, A136083, A136084, A136085, A136086, A136087, A136088, A136089, A136090, A136091.

a023208 n = a023208_list !! (n-1)
a023208_list = filter ((== 1) . a010051 . (+ 2) . (* 3)) a000040_list
-- Reinhard Zumkeller, Aug 15 2011

[n: n in PrimesUpTo(900) | IsPrime(3*n+2)]; // Vincenzo Librandi, Nov 20 2010

n = 1; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a (* Artur Jasinski, Dec 12 2007 *)

isA023208(n) = isprime(n) && isprime(3*n+2) \\ Michael B. Porter, Jan 30 2010

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar

A136082 Son primes of order 5.

Original entry on oeis.org

3, 11, 17, 23, 41, 53, 59, 107, 131, 167, 173, 179, 191, 257, 263, 269, 389, 401, 431, 461, 467, 479, 521, 563, 569, 599, 647, 653, 677, 683, 719, 773, 821, 839, 857, 887, 947, 971, 1031, 1049, 1061, 1091, 1103, 1151, 1181, 1217, 1223, 1259, 1277, 1301

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235.

Numbers in this sequence are those primes p such that 11*p + 10 is also prime. Generally, son primes of order n are the primes p such that (2n+1)*p + 2n is also prime. - Bob Selcoe, Apr 04 2015

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136083, A136084, A136085, A136086, A136087, A136088, A136089, A136090, A136091.

n = 5; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a
q=10;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 10 2009 *)
Select[Prime[Range[250]],PrimeQ[11#+10]&] (* Harvey P. Dale, Aug 07 2021 *)

A136084 Son primes of order 7.

Original entry on oeis.org

3, 5, 11, 17, 23, 29, 31, 37, 43, 47, 53, 61, 67, 73, 83, 103, 107, 113, 131, 137, 139, 163, 173, 179, 181, 191, 193, 197, 199, 223, 229, 251, 269, 271, 281, 283, 293, 311, 353, 359, 367, 389, 401, 419, 421, 439, 443, 457, 463, 467, 499, 503, 509, 521, 547, 557

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083.

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136085, A136086, A136087, A136088, A136089, A136090, A136091.

n = 7; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a
q=14;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 10 2009 *)

A136085 Son primes of order 8.

Original entry on oeis.org

3, 5, 29, 59, 71, 83, 101, 131, 149, 173, 239, 251, 281, 311, 401, 443, 449, 461, 491, 509, 563, 569, 653, 701, 719, 743, 761, 929, 953, 1109, 1151, 1193, 1223, 1259, 1289, 1301, 1373, 1451, 1511, 1553, 1571, 1583, 1613, 1619, 1811, 1913, 1931, 1949, 2039

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084.

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136086, A136087, A136088, A136089, A136090, A136091.

n = 8; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a
q=16;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 10 2009 *)

A136086 Son primes of order 9.

Original entry on oeis.org

5, 7, 11, 19, 29, 31, 41, 47, 67, 71, 89, 97, 109, 137, 139, 151, 157, 167, 181, 197, 211, 241, 251, 271, 277, 307, 311, 337, 367, 379, 397, 409, 421, 509, 557, 571, 587, 599, 601, 607, 619, 631, 641, 659, 661, 691, 701, 719, 727, 757, 769, 797, 811, 827, 839

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085.

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136087, A136088, A136089, A136090, A136091.

n = 9; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a
q=18;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 10 2009 *)

A136087 Son primes of order 10.

Original entry on oeis.org

3, 7, 11, 13, 19, 23, 37, 41, 59, 61, 67, 71, 73, 89, 101, 107, 109, 113, 127, 137, 139, 151, 167, 179, 181, 193, 197, 211, 223, 227, 239, 241, 257, 269, 271, 293, 311, 331, 347, 349, 353, 359, 367, 373, 409, 419, 421, 439, 443, 463, 479, 487, 491, 499, 509

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 8 see A136086.

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136088, A136089, A136090, A136091.

n = 10; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a
q=20;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 10 2009 *)

A136088 Son primes of order 11.

Original entry on oeis.org

5, 47, 83, 89, 113, 149, 167, 173, 179, 233, 239, 293, 383, 389, 443, 569, 587, 599, 683, 797, 839, 947, 1013, 1019, 1097, 1103, 1223, 1229, 1259, 1283, 1289, 1373, 1409, 1427, 1439, 1493, 1499, 1523, 1559, 1913, 1997, 2003, 2027, 2039, 2069, 2087, 2099

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136086.

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136087, A136089, A136090, A136091.

n = 11; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a

A136089 Son primes of order 12.

Original entry on oeis.org

5, 7, 13, 17, 19, 23, 41, 59, 61, 67, 79, 83, 101, 107, 109, 131, 137, 139, 163, 173, 181, 191, 199, 229, 233, 251, 257, 263, 277, 293, 307, 317, 347, 353, 359, 367, 373, 389, 397, 419, 431, 461, 467, 521, 523, 569, 577, 587, 607, 613, 653, 683, 691, 709, 727

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136087. For son primes of order 11 see A136088.

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136087, A136088, A136090, A136091.

n = 12; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a

A136090 Son primes of order 13.

Original entry on oeis.org

3, 23, 29, 31, 43, 59, 73, 83, 101, 109, 139, 149, 193, 199, 223, 233, 251, 263, 293, 311, 331, 359, 379, 389, 401, 409, 421, 433, 443, 449, 461, 463, 479, 499, 541, 563, 571, 601, 641, 643, 653, 739, 769, 773, 821, 823, 829, 839, 853, 863, 881, 911, 991, 1019

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136087. For son primes of order 11 see A136088. For son primes of order 12 see A136088.

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136087, A136088, A136089, A136091.

n = 13; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a

A136091 Son primes of order 14.

Original entry on oeis.org

5, 11, 17, 41, 71, 89, 101, 137, 149, 167, 197, 239, 251, 257, 269, 317, 347, 401, 431, 449, 461, 521, 569, 617, 641, 659, 677, 701, 719, 839, 881, 1031, 1049, 1091, 1109, 1277, 1289, 1367, 1427, 1439, 1487, 1499, 1571, 1601, 1637, 1667, 1721, 1847, 1871

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136087. For son primes of order 11 see A136088. For son primes of order 12 see A136089. For son primes of order 13 see A136090.

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

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136087, A136088, A136089, A136090.

n = 14; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a

cp's OEIS Frontend

A023208 Primes p such that 3*p + 2 is also prime.

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A136082 Son primes of order 5.

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A136084 Son primes of order 7.

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A136085 Son primes of order 8.

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A136086 Son primes of order 9.

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A136087 Son primes of order 10.

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A136088 Son primes of order 11.

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A136089 Son primes of order 12.

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A136090 Son primes of order 13.

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