A092109 -id:A092109 - cp's OEIS frontend

A145471 Primes p such that (5+p)/2 is prime.

5, 17, 29, 41, 53, 89, 101, 113, 137, 173, 197, 257, 269, 293, 353, 389, 449, 461, 509, 521, 557, 617, 701, 761, 773, 797, 857, 881, 929, 953, 977, 1013, 1109, 1181, 1193, 1229, 1277, 1289, 1301, 1361, 1433, 1481, 1613, 1637, 1709, 1721, 1877, 1889, 1901

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

All these primes are congruent to 1 mod 4 and to 5 mod 12.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A063909, A092109.

Subsequence of A040117. - Zak Seidov, Feb 21 2016

[p: p in PrimesInInterval(3,2000) | IsPrime((5+p) div 2)]; // Vincenzo Librandi, Feb 25 2016

select(t -> isprime(t) and isprime((t+5)/2), [seq(i, i=5..1000, 12)]); # Robert Israel, Feb 24 2016

aa = {}; k = 5; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(5+#)/2]&]  (* Harvey P. Dale, Apr 23 2011 *)

forprime(p=2,1e4,if(p%12!=5,next);if(isprime(p\2+3),print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2011

a(n) = 2*A063909(n)-5. - Robert Israel, Feb 24 2016

A145480 Primes p such that (p+37)/2 is prime.

Original entry on oeis.org

37, 97, 109, 157, 181, 241, 277, 349, 409, 421, 577, 661, 709, 757, 829, 877, 937, 1009, 1117, 1201, 1249, 1381, 1429, 1609, 1621, 1669, 1777, 1801, 2029, 2089, 2137, 2221, 2269, 2389, 2437, 2521, 2557, 2617, 2857, 3049, 3061, 3121, 3181, 3217, 3301, 3361

Offset: 1

Artur Jasinski, Oct 11 2008

All these primes are congruent to 1 mod 12

Harvey P. Dale, Table of n, a(n) for n = 1..1000

A092109, A145471-A145480.

aa = {}; k = 37; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(37+#)/2]&] (* Harvey P. Dale, Jun 23 2016 *)

list(n)=my(t=1, p, i=1); while(i2&&isprime((37+p)/2), print(p,", "))) \\Anders Hellström, Jan 23 2017

list(lim)=my(v=List()); forprime(p=3,lim, if(isprime((p+37)/2), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

a(n) >> n log^2 n. - Charles R Greathouse IV, Jan 23 2017

A145490 Numbers k such that 6k+19 is prime and absolute value of 12k+1 is also prime.

Original entry on oeis.org

-2, -1, 3, 8, 9, 13, 15, 20, 23, 29, 34, 35, 48, 55, 59, 63, 69, 73, 78, 84, 93, 100, 104, 115, 119, 134, 135, 139, 148, 150, 169, 174, 178, 185, 189, 199, 203, 210, 213, 218, 238, 254, 255, 260, 265, 268, 275, 280, 288, 289, 293, 294, 295, 308, 309, 335, 344

Offset: 1

Artur Jasinski, Oct 11 2008

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A063908-A063913, A092109, A145471-A145490.

with(numtheory): a:=proc(n) if(isprime(6*n+19) and isprime(abs(12*n+1)))then return n: fi: return NULL: end: seq(a(n),n=-2..350); # Nathaniel Johnston, Jul 26 2011

a(n) = (A145480(n-2)-1)/12 for n >= 3.

Corrected by Arkadiusz Wesolowski, Jul 26 2011

A092110 Primes p such that 2p+3 and 2p-3 are both prime.

Original entry on oeis.org

5, 7, 13, 17, 43, 53, 67, 97, 113, 127, 137, 157, 167, 193, 223, 283, 487, 547, 563, 613, 617, 643, 647, 743, 773, 937, 1033, 1187, 1193, 1277, 1427, 1453, 1483, 1543, 1583, 1627, 1663, 1733, 1847, 2027, 2143, 2297, 2393, 2437, 2467, 2477, 2503, 2617, 2843

Offset: 1

Zak Seidov, Feb 21 2004

Intersection of A023204 and A063908.

All numbers in this sequence end with 3 or 7 (except the first one, which is 5). See A136191 or A136192. - Carlos Alves, Dec 20 2007

			From _K. D. Bajpai_, Sep 08 2020: (Start)
7 is a term because 2*7 + 3 = 17 and 2*7 - 3 = 11 are both prime.
13 is a term because 2*13 + 3 = 29 and 2*13 - 3 = 23 are both prime.
(End)

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A023204, A089531, A063908, A092109.

Cf. A136191, A136192.

[p: p in PrimesUpTo(10000)|IsPrime(2*p-3) and IsPrime(2*p+3)] // Vincenzo Librandi, Nov 16 2010

select(p -> isprime(p) and isprime(2*p+3) and isprime(2*p-3), [seq(2*k+1, k=1..1000)]); # K. D. Bajpai, Sep 08 2020

Select[Prime@Range@1000,PrimeQ[2#-3]&&PrimeQ[2#+3]&] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2011 *)

A145475 Primes p such that (17+p)/2 is prime.

Original entry on oeis.org

5, 17, 29, 41, 89, 101, 149, 197, 257, 281, 317, 449, 461, 509, 521, 569, 617, 677, 701, 761, 821, 881, 941, 1097, 1109, 1181, 1217, 1277, 1289, 1301, 1601, 1637, 1697, 1709, 1877, 1889, 1949, 2081, 2309, 2357, 2417, 2441, 2549, 2621, 2729, 2801, 2837, 2861

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

All these primes are congruent to 5 mod 12.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A092109, A145471-A145480.

aa = {}; k = 17; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(17+#)/2]&] (* Harvey P. Dale, Jan 02 2013 *)

A145472 Primes p such that (p+7)/2 is prime.

Original entry on oeis.org

3, 7, 19, 31, 67, 79, 127, 139, 151, 199, 211, 271, 307, 379, 439, 547, 607, 619, 691, 727, 739, 751, 787, 811, 859, 907, 919, 967, 991, 1039, 1087, 1231, 1279, 1447, 1459, 1471, 1531, 1567, 1699, 1747, 1759, 1831, 1867, 1987, 2011, 2131, 2179, 2239, 2251

Offset: 1

Artur Jasinski, Oct 11 2008

All these primes are congruent to 3 mod 4 and (with the exception of the first one) to 7 mod 12.

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

Cf. A092109, A145471-A145480, A063910.

[p: p in PrimesUpTo(2500)| IsPrime((p + 7) div 2)]; // Vincenzo Librandi, Feb 04 2013

aa = {}; k = 7; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(#+7)/2]&] (* Harvey P. Dale, Jan 11 2020 *)

list(n)=my(t=1, p, i=1); while(i2&&isprime((7+p)/2), print1(n, ", "))) \\Anders Hellström, Jan 23 2017

list(lim)=my(v=List()); forprime(p=3,lim, if(isprime((p+7)/2), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

A145474 Primes p such that (13+p)/2 is prime.

Original entry on oeis.org

13, 61, 73, 109, 181, 193, 241, 313, 349, 373, 409, 433, 541, 601, 613, 661, 733, 829, 853, 1033, 1069, 1129, 1201, 1213, 1249, 1453, 1489, 1609, 1693, 1741, 1753, 1801, 1861, 2029, 2053, 2089, 2113, 2161, 2221, 2293, 2389, 2593, 2749, 2833, 2953, 3049

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

All these primes are congruent to 1 mod 12.

Edward Jiang, Table of n, a(n) for n = 1..10000

Cf. A092109, A145471-A145480.

select(t -> isprime(t) and isprime((13+t)/2), [seq(12*k+1, k=1..100)]); # Robert Israel, Aug 05 2014

aa = {}; k = 13; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa

forprime(p=3,10^4,if(isprime((13+p)/2),print1(p,", "))) \\ Derek Orr, Aug 05 2014

A145476 Primes p such that (19 + p)/2 is prime.

Original entry on oeis.org

3, 7, 19, 43, 67, 103, 127, 139, 199, 283, 307, 367, 379, 439, 463, 523, 547, 607, 643, 727, 739, 823, 859, 907, 1063, 1123, 1303, 1327, 1399, 1447, 1459, 1483, 1627, 1699, 1747, 1999, 2083, 2239, 2287, 2383, 2539, 2887, 3067, 3079, 3307, 3319, 3463, 3499

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 5 mod 12.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A092109, A145471-A145480.

aa = {}; k = 19; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(#+19)/2]&] (* Harvey P. Dale, Sep 06 2023 *)

list(n)=my(t=1,p,i=1);while(i2&&bigomega((19+p)/2)==1,print(p))) \\ Anders Hellström, Jan 22 2017

A145477 Primes p such that (23 + p)/2 is prime.

Original entry on oeis.org

3, 11, 23, 59, 71, 83, 179, 191, 239, 251, 311, 359, 431, 443, 479, 491, 503, 563, 599, 683, 743, 839, 863, 911, 983, 1019, 1091, 1103, 1151, 1163, 1259, 1283, 1499, 1523, 1571, 1619, 1871, 1931, 2003, 2039, 2099, 2339, 2351, 2411, 2423, 2531, 2543, 2579

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 11 mod 12.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A092109, A145471-A145480.

aa = {}; k = 23; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(23+#)/2]&] (* Harvey P. Dale, Jan 26 2024 *)

list(n)=my(t=1, p, i=1); while(i2&&prime((23+p)/2), print1(p, ", "))) \\ Anders Hellström, Jan 23 2017

A145478 Primes p such that (29 + p)/2 is prime.

Original entry on oeis.org

5, 17, 29, 53, 89, 113, 137, 149, 173, 197, 233, 269, 317, 353, 449, 509, 557, 593, 677, 773, 809, 857, 929, 953, 977, 1013, 1097, 1109, 1277, 1289, 1373, 1409, 1493, 1613, 1697, 1733, 1877, 1913, 1997, 2069, 2153, 2273, 2297, 2333, 2357, 2417, 2549, 2609

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

All these primes are congruent to 5 mod 12.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A092109, A145471-A145480.

aa = {}; k = 29; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa

first(n)=my(t=1, p, i=1); while(i2&&isprime((29+p)/2), print1(p,", "))) \\ Anders Hellström, Jan 22 2017

cp's OEIS Frontend

A145471 Primes p such that (5+p)/2 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A145480 Primes p such that (p+37)/2 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A145490 Numbers k such that 6k+19 is prime and absolute value of 12k+1 is also prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Formula

Extensions

A092110 Primes p such that 2p+3 and 2p-3 are both prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

A145475 Primes p such that (17+p)/2 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A145472 Primes p such that (p+7)/2 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

PARI

A145474 Primes p such that (13+p)/2 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI