A063913 -id:A063913 - cp's OEIS frontend

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

-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

A145487 Numbers k such that 6k+5 is prime and 12k+5 is also prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 9, 11, 14, 16, 21, 22, 24, 29, 32, 37, 38, 42, 43, 46, 51, 58, 63, 64, 66, 71, 73, 77, 79, 81, 84, 92, 98, 99, 102, 106, 107, 108, 113, 119, 123, 134, 136, 142, 143, 156, 157, 158, 162, 184, 191, 196, 198, 203, 212, 217, 219, 227, 228, 238, 241, 246

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

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

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

aa = {}; k = 5; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (Prime[n] - 5)/12]], {n, 1, 500}]; aa
Select[Range[0, 250], PrimeQ[6 # + 5] && PrimeQ[12 # + 5] &] (* Ivan Neretin, Jan 21 2017 *)
Select[Range[0,250],AllTrue[5+{6#,12#},PrimeQ]&] (* Harvey P. Dale, Dec 20 2022 *)

a(n) = (A145471(n)-5)/12.

A290838 a(n) = smallest prime p such that 2p - 2n + 1 is prime.

Original entry on oeis.org

2, 2, 3, 5, 5, 7, 7, 13, 11, 11, 11, 13, 13, 19, 17, 17, 17, 19, 19, 37, 23, 23, 23, 29, 29, 31, 29, 29, 29, 31, 31, 37, 37, 41, 37, 37, 37, 43, 41, 41, 41, 43, 43, 61, 47, 47, 47, 53, 53, 67, 53, 53, 53, 59, 59, 61, 59, 59, 59, 61, 61, 67, 67, 71, 67, 67, 67, 73

Offset: 0

XU Pingya, Aug 11 2017

a(n) > n. - Iain Fox, Nov 13 2017

Iain Fox, Table of n, a(n) for n = 0..20000

Cf. A005382, A063908, A063909, A063910, A063911, A063912, A063913, A020483, A290839.

Table[j=0; found=False; While[!found,j++; found=PrimeQ[2Prime[j]-2n+1] && 2Prime[j]-2n+1>0]; Prime[j],{n,67}]
(* Second program: *)
Table[SelectFirst[Prime@ Range[n^2], And[# > 0, PrimeQ@ #] &[2 # - 2 n + 1] &], {n, 67}] (* Michael De Vlieger, Aug 14 2017 *)

a(n) = {my(p=2); while(!isprime(2*p-2*n+1), p = nextprime(p+1)); p; } \\ Michel Marcus, Aug 12 2017

a(n) = forprime(p=n+1, , if(isprime(2*p - 2*n + 1), return(p))) \\ Iain Fox, Nov 13 2017

a(-n) = A290839(n+1) - Iain Fox, Dec 14 2017

a(0) prepended by Iain Fox, Dec 14 2017

A337480 Numbers k such that exactly one of 6k + 5 and 12k + 5 is prime.

Original entry on oeis.org

6, 12, 13, 17, 18, 19, 23, 26, 27, 28, 31, 33, 39, 41, 44, 47, 48, 49, 52, 53, 54, 56, 57, 59, 67, 68, 69, 74, 76, 78, 83, 86, 87, 88, 91, 93, 94, 97, 101, 109, 112, 114, 116, 117, 124, 126, 128, 129, 132, 133, 137, 139, 141, 144, 146, 147, 151, 154, 159, 161

Offset: 1

K. D. Bajpai, Aug 28 2020

nonn

			a(5) = 18 is a term because 6*18 + 5 = 113 is prime; but 12*18 + 5 = 221 = (13*17) is a composite number.
a(8) = 26 is a term because 6*26 + 5 = 161 = (7*23) is a composite number; but 12*26 + 5 = 317 is prime.

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

Cf. A063913, A145487, A145490, A172287.

A337480:=k->`if`(isprime(6*k+5) xor isprime(12*k+5),k, NULL): seq(A337480(k), k=1..1000);

Select[Range[0, 250], Xor[PrimeQ[6 # + 5], PrimeQ[12 # + 5]] &]

for(k=1, 1000, if (bitxor(isprime(6*k+5), isprime(12*k+5)), print1(k, ", ")));

A145481 Primes p such that 2*p - 17 is prime.

Original entry on oeis.org

11, 17, 23, 29, 53, 59, 83, 107, 137, 149, 167, 233, 239, 263, 269, 293, 317, 347, 359, 389, 419, 449, 479, 557, 563, 599, 617, 647, 653, 659, 809, 827, 857, 863, 947, 953, 983, 1049, 1163, 1187, 1217, 1229, 1283, 1319, 1373, 1409, 1427, 1439, 1487, 1493

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

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

Cf. A063908-A063913, A092109, A145471-A145480.

aa = {}; k = 17; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 250, And[PrimeQ@ #, # > 0] &[2 # - 17] &] (* Michael De Vlieger, Jan 23 2017 *)

a(n) = 2*A145475(n) - 17.

A145482 Primes p such that 2*p - 19 is prime.

Original entry on oeis.org

11, 13, 19, 31, 43, 61, 73, 79, 109, 151, 163, 193, 199, 229, 241, 271, 283, 313, 331, 373, 379, 421, 439, 463, 541, 571, 661, 673, 709, 733, 739, 751, 823, 859, 883, 1009, 1051, 1129, 1153, 1201, 1279, 1453, 1543, 1549, 1663, 1669, 1741, 1759, 1783, 1789

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

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

Cf. A063908-A063913, A092109, A145471-A145480.

aa = {}; k = 19; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 300, And[PrimeQ@ #, # > 0] &[2 # - 19] &] (* Michael De Vlieger, Jan 23 2017 *)

a(n) = 2*A145476(n) - 19.

A145483 Primes p such that 2*p - 23 is prime.

Original entry on oeis.org

13, 17, 23, 41, 47, 53, 101, 107, 131, 137, 167, 191, 227, 233, 251, 257, 263, 293, 311, 353, 383, 431, 443, 467, 503, 521, 557, 563, 587, 593, 641, 653, 761, 773, 797, 821, 947, 977, 1013, 1031, 1061, 1181, 1187, 1217, 1223, 1277, 1283, 1301, 1307, 1361

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

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

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

aa = {}; k = 23; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 240, And[PrimeQ@ #, # > 0] &[2 # - 23] &] (* Michael De Vlieger, Jan 23 2017 *)

a(n) = 2*A145477(n) - 23.

A145484 Primes p such that 2*p - 29 is a positive prime.

Original entry on oeis.org

17, 23, 29, 41, 59, 71, 83, 89, 101, 113, 131, 149, 173, 191, 239, 269, 293, 311, 353, 401, 419, 443, 479, 491, 503, 521, 563, 569, 653, 659, 701, 719, 761, 821, 863, 881, 953, 971, 1013, 1049, 1091, 1151, 1163, 1181, 1193, 1223, 1289, 1319, 1361, 1409

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

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

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

aa = {}; k = 29; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa (* Artur Jasinski *)
Select[Prime[Range[7,300]],PrimeQ[2#-29]&] (* Harvey P. Dale, Dec 14 2010 *)

a(n) = 2*A145478(n) - 29.

A145485 Primes p such that 2*p - 31 is prime.

Original entry on oeis.org

17, 19, 31, 37, 67, 79, 97, 127, 151, 157, 181, 199, 277, 331, 337, 379, 409, 421, 457, 499, 541, 547, 577, 601, 631, 661, 727, 739, 751, 757, 787, 829, 877, 907, 991, 1009, 1021, 1087, 1117, 1171, 1201, 1249, 1291, 1381, 1399, 1459, 1549, 1597, 1609, 1669

Offset: 1

Artur Jasinski, Oct 11 2008

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

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

aa = {}; k = 31; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa

list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(2*p-31), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

a(n) = 2*A145479(n) - 31.

A145486 Primes p such that 2*p - 37 is prime.

Original entry on oeis.org

37, 67, 73, 97, 109, 139, 157, 193, 223, 229, 307, 349, 373, 397, 433, 457, 487, 523, 577, 619, 643, 709, 733, 823, 829, 853, 907, 919, 1033, 1063, 1087, 1129, 1153, 1213, 1237, 1279, 1297, 1327, 1447, 1543, 1549, 1579, 1609, 1627, 1669, 1699, 1747, 1753

Offset: 1

Artur Jasinski, Oct 11 2008

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

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

aa = {}; k = 37; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa

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

a(n)=2*A145480(n)-37

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

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A145487 Numbers k such that 6k+5 is prime and 12k+5 is also prime.

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A290838 a(n) = smallest prime p such that 2p - 2n + 1 is prime.

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A337480 Numbers k such that exactly one of 6*k + 5 and 12*k + 5 is prime.

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A145481 Primes p such that 2*p - 17 is prime.

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A145482 Primes p such that 2*p - 19 is prime.

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A145483 Primes p such that 2*p - 23 is prime.

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A145484 Primes p such that 2*p - 29 is a positive prime.

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A337480 Numbers k such that exactly one of 6k + 5 and 12k + 5 is prime.