cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-28 of 28 results.

A145488 Numbers k such that 6k+13 is prime and 12k+13 is also prime.

Original entry on oeis.org

0, 4, 5, 8, 14, 15, 19, 25, 28, 30, 33, 35, 44, 49, 50, 54, 60, 68, 70, 85, 88, 93, 99, 100, 103, 120, 123, 133, 140, 144, 145, 149, 154, 168, 170, 173, 175, 179, 184, 190, 198, 215, 228, 235, 245, 253, 259, 264, 268, 274, 275, 280, 285, 288, 294
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Maple
    select(k -> isprime(6*k+13) and isprime(12*k+13), [$0..1000]); # Robert Israel, Jan 23 2017
  • Mathematica
    aa = {}; k = 13; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (Prime[n] - k)/12]], {n, 1, 500}]; aa

Formula

a(n) = (A145474(n)-13)/12.

Extensions

Definition corrected by Ivan Neretin, Jan 23 2017

A145489 Numbers k such that 6k + 11 is prime and 12k + 5 is also prime.

Original entry on oeis.org

0, 1, 2, 3, 7, 8, 12, 16, 21, 23, 26, 37, 38, 42, 43, 47, 51, 56, 58, 63, 68, 73, 78, 91, 92, 98, 101, 106, 107, 108, 133, 136, 141, 142, 156, 157, 162, 173, 192, 196, 201, 203, 212, 218, 227, 233, 236, 238, 246, 247, 257, 267, 268, 271, 287, 296, 306, 313, 316, 323, 327, 332, 346, 353, 357, 366, 367, 371, 376, 387, 401, 406, 411, 423, 441, 442, 448, 453, 471, 472, 478, 483, 488, 491, 498
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0,500], PrimeQ[6# + 11 ] && PrimeQ[12# + 5]&]
  • PARI
    isok(n) = isprime(6*n+11) && isprime(12*n+5); \\ Michel Marcus, Jan 24 2017

Formula

a(n) = (A145475(n) - 5)/12.

Extensions

Corrected by Artur Jasinski, Apr 01 2011

A171518 Primes p such that 3*p-+8 are primes.

Original entry on oeis.org

5, 7, 13, 17, 53, 73, 83, 113, 127, 157, 193, 223, 277, 347, 367, 433, 613, 647, 673, 743, 797, 907, 937, 1117, 1217, 1373, 1427, 1483, 1543, 1597, 1637, 1667, 1877, 1933, 2027, 2237, 2297, 2447, 2647, 2687, 2843, 3083, 3137, 3613, 3797, 4073, 4463, 4483
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 10 2009

Keywords

Examples

			5 is in the sequence since 3*5-8=7 and 3*5+8=23 are primes.

Links

Crossrefs

Cf. A000040, A005382, A005384, A023204-A023207, A063908-A063912, A103803, A124098, A125272, A171517

Programs

  • Mathematica
    Select[Prime[Range[7! ]],PrimeQ[3*#-8]&&PrimeQ[3*#+8]&]
Select[Prime[Range[700]],AllTrue[3#+{8,-8},PrimeQ]&] (* Harvey P. Dale, Feb 10 2025 *)

A171566 Primes p such that 2*p-3 and 2*(2*p-3)-3 are primes (First member of a primes in a 2*p-3 double progression).

Original entry on oeis.org

3, 5, 7, 13, 17, 23, 37, 43, 97, 107, 113, 127, 157, 167, 223, 283, 317, 373, 433, 547, 563, 587, 617, 647, 743, 757, 773, 937, 1123, 1277, 1297, 1423, 1483, 1487, 1543, 1583, 1597, 1667, 1697, 1823, 1913, 1933, 1973, 2137, 2143, 2243, 2333, 2437, 2467
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 11 2009

Keywords

Examples

			2*3-3=3, 2*5-3=7; 2*7-3=11, 2*7-3=11; 2*11-3=19,..

References

  • Mohammad K. Azarian, Double Progression, Problem 231, Math Horizons, Vol. 16, Issue 4, April 2009, p. 31. Solution published in Vol. 17, Issue 2, November 2009, p. 32.

Links

Crossrefs

Cf. A063908

Programs

  • Mathematica
    Select[Prime[Range[7! ]],PrimeQ[2*#-3]&&PrimeQ[2*(2*#-3)-3]&]
Select[Prime[Range[400]],AllTrue[{2#-3,4#-9},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 04 2021 *)

A173269 2*prime(prime(n))-3 and 3*prime(prime(n))-2 are both primes.

Original entry on oeis.org

1, 2, 3, 8, 11, 14, 15, 19, 23, 24, 28, 39, 44, 47, 54, 62, 63, 81, 85, 101, 121, 122, 124, 136, 152, 159, 180, 218, 219, 241, 247, 253, 274, 290, 298, 307, 323, 324, 341, 361, 371, 376, 381, 403, 410, 413, 441, 443, 479, 487, 499, 552, 554, 556, 562, 582, 622
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 14 2010

Keywords

Examples

			a(1)=1 because 2*p(p(1))-3=2*p(2)-3=2*3-3=3=prime and 3*p(p(1))-2=7=prime; a(2)=2 because 2*p(p(2))-3=2*p(3)-3=2*5-3=7=prime and 3*p(p(2))-2=13=prime; a(3)=3 because 2*p(p(3))-3=2*p(5)-3=2*11-3=19=prime and 3*p(p(3))-2=31=prime; a(4)=8 because 2*p(p(8))-3=2*p(19)-3=2*67-3=131=prime and 3*p(p(8))-2=199=prime.

Crossrefs

Cf. A063908, A088878.

Extensions

Inserted 23 and 24, removed 34, extended the sequence - R. J. Mathar, Mar 01 2010

A173286 2*prime(prime(prime(n)))-3 and 3*prime(prime(prime(n)))-2 are both primes.

Original entry on oeis.org

1, 2, 5, 8, 9, 15, 26, 53, 63, 86, 92, 93, 95, 116, 137, 152, 233, 254, 281, 303, 329, 334, 352, 386, 392, 415, 423, 460, 470, 476, 508, 565, 570, 601, 660, 673, 680, 725, 748, 898, 907, 942, 948, 952, 958, 1045, 1119, 1126, 1138, 1140, 1259, 1314, 1360
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 15 2010

Keywords

Examples

			a(1) = 1 because 2*p(p(p(1)))-3 = 7 = prime and 3*p(p(p(1)))-2 = 13 = prime;
a(2) = 2 because 2*p(p(p(2)))-3 = 19 = prime and 3*p(p(p(2)))-2 = 31 = prime;
a(3) = 5 because 2*p(p(p(5)))-3 = 379 = prime and 3*p(p(p(5)))-2 = 251 = prime;
a(4) = 8 because 2*p(p(p(8)))-3 = 991 = prime and 3*p(p(p(8)))-2 = 659 = prime;
a(5) = 9 because 2*p(p(p(9)))-3 = 1291 = prime and 3*p(p(p(9)))-2 = 859 = prime;
a(6) = 15 because 2*p(p(p(15)))-3 = 3889 = prime and 3*p(p(p(15)))-2 = 2591 = prime.

Crossrefs

Cf. A038580, A063908, A088878.

Programs

  • Mathematica
    pppQ[n_]:=Module[{p=Prime[Prime[Prime[n]]]},AllTrue[{2p-3,3p-2},PrimeQ]]; Select[Range[1400],pppQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 25 2016 *)
  • PARI
    isok(n) = isprime(2*prime(prime(prime(n)))-3) && isprime(3*prime(prime(prime(n)))-2); \\ Michel Marcus, Sep 02 2013

Extensions

Extended beyond 15 by R. J. Mathar, Mar 01 2010

A337491 Numbers k such that exactly one of 2*k + 3 and 4*k + 3 is prime.

Original entry on oeis.org

8, 11, 13, 16, 22, 26, 28, 29, 31, 35, 37, 38, 41, 43, 44, 50, 53, 56, 59, 64, 65, 68, 70, 73, 74, 76, 80, 85, 86, 88, 91, 97, 98, 107, 109, 112, 113, 116, 118, 121, 122, 125, 127, 133, 134, 136, 137, 139, 142, 145, 146, 149, 151, 152, 155, 160, 161, 167, 170
Offset: 1

Views

Author

K. D. Bajpai, Aug 29 2020

Keywords

Comments

Integers that are in A067076 or in A095278, but not in both. - Michel Marcus, Aug 29 2020

Examples

			a(1) = 8 is a term because 2*8 + 3 = 19 is a prime; but 4*8 + 3 = 35 = (5*7) is a composite number.
a(4) = 16 is a term because 2*16 + 3 = 35 = (5*7) is a composite number; but 4*16 + 3 = 67  is a prime.
a(6) = 26 is a term because 2*26 + 3 = 55 = (5*11) is a composite number; but 4*26 + 3 = 107  is a prime.

Links

Crossrefs

Cf. A063908, A067076, A095278, A337480.

Programs

  • Maple
    A337491:=n->`if`((isprime(2*n+3) xor isprime(4*n+3)), n, NULL): seq(A337491(n), n=1..500);
  • Mathematica
    Select[Range[0, 250], Xor[PrimeQ[2 # + 3], PrimeQ[4 # + 3]] &]
Select[Range[200],Total[Boole[PrimeQ[{2,4}#+3]]]==1&] (* Harvey P. Dale, Jan 26 2023 *)
  • PARI
    isok(k) = bitxor(isprime(2*k+3), isprime(4*k+3)); \\ Michel Marcus, Aug 29 2020

A173287 Intersection of A173286 and A173269.

Original entry on oeis.org

1, 2, 8, 15, 63, 152, 2306, 2373
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 15 2010

Keywords

Examples

			a(1)=1 because 2*p(p(p(1)))-3=7=prime, 2*p(p(1))-3=3=prime and 3*p(p(p(1)))-2=13=prime, 3*p(p(1))-2=7=prime; a(2)=2 because 2*p(p(p(2)))-3=19=prime, 3p(p(2))-2=13=prime and 3*p(p(p(2)))-2=31=prime, 3*p(p(2))-2=13=prime; a(3)=8 because 2*p(p(p(8)))-3=991=prime, 2*p(p(8))-3=199=prime and 3*p(p(p(8)))-2=659=prime, 3*p(p(8))-2=131=prime; a(4)=15 because 2*p(p(p(15)))-3=3889=prime, 3*p(p(15))-2=631=prime and 3*p(p(p(15)))-2=2591=prime, 2*p(p(15))-3=439=prime.

Crossrefs

Cf. A038580, A063908, A088878.

Extensions

Definition corrected and 4 terms appended by R. J. Mathar, Mar 01 2010
Previous Showing 21-28 of 28 results.

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